9\. Reference Tables

Table 9.1 Use of Range to Estimate Standard Deviation

Table 9.2 Z Factors for Two-sided Confidence Intervals

Table 9.3 Student t-Variate

Table 9.4 Critical Values for the F-test, F~0.975~

Table 9.5 Critical Values for the F-test, F~0.99~

Table 9.6 Two-sided Tolerance Interval Factors

Table 9.7 Factors for Computing Two-sided Confidence Intervals for

Table 9.8 Density of Air-free Water

Table 9.9 Density of Air

Table 9.10 Coefficient of Linear and Cubical Expansion for Materials
Commonly Used in Laboratory Apparatus and Standards

Table 9.11 A Short Table of Random Numbers

Table 9.1 Use of Range to Estimate Standard Deviation

+---------+---------+---------+---------+---------+---------+---------+
| Number  | [Facto  | # N     |         |         |         |         |
| of      | r]{.und | umber o |         |         |         |         |
|         | erline} | f Repli |         |         |         |         |
| Sets of |         | cates i |         |         |         |         |
|         | Degrees | n a Set |         |         |         |         |
| Rep     | of      |         |         |         |         |         |
| licates |         |         |         |         |         |         |
|         | Freedom |         |         |         |         |         |
| k       |         |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         |         | 2       | 3       | 4       | 5       | 6       |
+---------+---------+---------+---------+---------+---------+---------+
| 1       | $d_     | 1.41    | 1.91    | 2.24    | 2.48    | 2.67    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 1.00    | 1.98    | 2.93    | 3.83    | 4.68    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 3       | $d_     | 1.23    | 1.77    | 2.12    | 2.38    | 2.58    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 2.83    | 5.86    | 8.44    | 11.1    | 13.6    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 5       | $d_     | 1.19    | 1.74    | 2.10    | 2.36    | 2.56    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 4.59    | 9.31    | 13.9    | 18.4    | 22.6    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 10      | $d_     | 1.16    | 1.72    | 2.08    | 2.34    | 2.55    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 8.99    | 18.4    | 27.6    | 36.5    | 44.9    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 15      | $d_     | 1.15    | 1.71    | 2.07    | 2.34    | 2.54    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 13.4    | 27.5    | 41.3    | 54.6    | 67.2    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 20      | $d_     | 1.14    | 1.70    | 2.07    | 2.33    | 2.54    |
|         | {2}^{}$ |         |         |         |         |         |
|         |         | 17.8    | 36.5    | 55.0    | 72.7    | 89.6    |
|         | > $\u   |         |         |         |         |         |
|         | psilon$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| ∞       | $d_     | 1.13    | 1.69    | 2.06    | 2.33    | 2.53    |
|         | {2}^{}$ |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| $$\     |         |         |         |         |         |         |
| frac{\o |         |         |         |         |         |         |
| verline |         |         |         |         |         |         |
| {R}}{d_ |         |         |         |         |         |         |
| {2}^{}} |         |         |         |         |         |         |
|  \right |         |         |         |         |         |         |
| arrow \ |         |         |         |         |         |         |
| sigma$$ |         |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+

Intermediate values for $d_{2}^{}$ and $\upsilon$ may be obtained by
interpolation, or from the reference from which this table was adapted.

Example: If 10 sets of measurements were made and each set consisted of
two measurements (duplicates), the value for $d_{2}^{}$ is 1.16; if 15
sets of measurements were made and each set consisted of three
measurements (triplicates) the value for $d_{2}^{}$ is 1.71.

Adapted from Lloyd S. Nelson, J. Qual. Tech. [7]{.underline} No. 1,
January 1975.

© 1975 American Society for Quality Control, Reprinted by permission.

**Table 9.2 Z‑Factors for Two‑sided Confidence Intervals**

**for the Normal Distribution**

+----------------------------------+-----------------------------------+
| Confidence Level, %              | Z Factor                          |
+----------------------------------+-----------------------------------+
| > 50                             | > 0.68                            |
+----------------------------------+-----------------------------------+
| > 67                             | > 1.00                            |
+----------------------------------+-----------------------------------+
| > 75                             | > 1.15                            |
+----------------------------------+-----------------------------------+
| > 90                             | > 1.645                           |
+----------------------------------+-----------------------------------+
| > 95                             | > 1.960                           |
+----------------------------------+-----------------------------------+
| > 95.28                          | > 2.000                           |
+----------------------------------+-----------------------------------+
| > 99.00                          | > 2.575                           |
+----------------------------------+-----------------------------------+
| > 99.74                          | > 3                               |
+----------------------------------+-----------------------------------+
| > 99.993 4                       | > 4                               |
+----------------------------------+-----------------------------------+
| > 99.999 95                      | > 5                               |
+----------------------------------+-----------------------------------+
| > 100 - 10^-9^                   | > 6                               |
+----------------------------------+-----------------------------------+
| > 100 - 10^-12^                  | > 7                               |
+----------------------------------+-----------------------------------+
| > 100 - 10^-15^                  | > 8                               |
+----------------------------------+-----------------------------------+
| > 100 - 10^-18.9^                | > 9                               |
+----------------------------------+-----------------------------------+
| > 100 - 10^-23^                  | > 10                              |
+----------------------------------+-----------------------------------+

**Table 9.3 Student t‑Variate**

  ---------- ---------- ---------- ---------- ---------- ---------- -----------
  \*         80 %       90 %       95 %       98 %       99 %       99.73 %

  df         t~0.90~    t~0.95~    t~0.975~   t~0.99~    t~0.995~   t~0.9985~

  1          3.078      6.314      12.706     31.821     63.657     235.80

  2          1.886      2.920      4.303      6.965      9.925      19.207

  3          1.638      2.353      3.182      4.541      5.841      9.219

  4          1.533      2.132      2.776      3.747      4.604      6.620

  5          1.476      2.015      2.571      3.365      4.032      5.507

  6          1.440      1.943      2.447      3.143      3.707      4.904

  7          1.415      1.895      2.365      2.998      3.499      4.530

  8          1.397      1.860      2.306      2.896      3.355      4.277

  9          1.383      1.833      2.262      2.821      3.250      4.094

  10         1.372      1.812      2.228      2.764      3.169      3.957

  11         1.363      1.796      2.201      2.718      3.106      3.850

  12         1.356      1.782      2.179      2.681      3.055      3.764

  13         1.350      1.771      2.160      2.650      3.012      3.694

  14         1.345      1.761      2.145      2.624      2.977      3.636

  15         1.341      1.753      2.131      2.602      2.947      3.586

  16         1.337      1.746      2.120      2.583      2.921      3.544

  17         1.333      1.740      2.110      2.567      2.898      3.507

  18         1.330      1.734      2.101      2.552      2.878      3.475

  19         1.328      1.729      2.093      2.539      2.861      3.447

  20         1.325      1.725      2.086      2.528      2.845      3.422

  25         1.316      1.708      2.060      2.485      2.787      3.330

  30         1.310      1.697      2.042      2.457      2.750      3.270

  40         1.303      1.684      2.021      2.423      2.704      3.199

  60         1.296      1.671      2.000      2.390      2.660      3.130

  ∞          1.282      1.645      1.960      2.326      2.576      3.00
  ---------- ---------- ---------- ---------- ---------- ---------- -----------

\* Columns to be used in calculating corresponding two-sided confidence
interval. From: NBS Handbook 91 p. T-5; Last column from B.J. Joiner, J.
Research NBS.

**Table 9.4 Critical values for the F‑Test, F~0.975~**

n~1~ = degrees of freedom for numerator n~2~ = degrees of freedom for
denominator

<table style="width:100%;">
<colgroup>
<col style="width: 6%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 5%" />
</colgroup>
<tbody>
<tr class="odd">
<td><p>n1</p>
<p>n2</p></td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
<td>9</td>
<td>10</td>
<td>12</td>
<td>15</td>
<td>20</td>
<td>24</td>
<td>30</td>
<td>40</td>
</tr>
<tr class="even">
<td>1</td>
<td>647.8</td>
<td>799.5</td>
<td>864.2</td>
<td>899.6</td>
<td>921.8</td>
<td>937.1</td>
<td>948.2</td>
<td>956.7</td>
<td>963.3</td>
<td>968.6</td>
<td>976.7</td>
<td>984.9</td>
<td>993.1</td>
<td>997.2</td>
<td>1001</td>
<td>1006</td>
</tr>
<tr class="odd">
<td>2</td>
<td>38.51</td>
<td>39.00</td>
<td>39.17</td>
<td>39.25</td>
<td>39.30</td>
<td>39.33</td>
<td>39.36</td>
<td>39.37</td>
<td>39.39</td>
<td>39.40</td>
<td>39.41</td>
<td>39.43</td>
<td>39.45</td>
<td>39.46</td>
<td>39.46</td>
<td>39.47</td>
</tr>
<tr class="even">
<td>3</td>
<td>17.44</td>
<td>16.04</td>
<td>15.44</td>
<td>15.10</td>
<td>14.88</td>
<td>14.73</td>
<td>14.62</td>
<td>14.54</td>
<td>14.47</td>
<td>14.42</td>
<td>14.34</td>
<td>14.25</td>
<td>14.17</td>
<td>14.12</td>
<td>14.08</td>
<td>14.04</td>
</tr>
<tr class="odd">
<td>4</td>
<td>12.22</td>
<td>10.65</td>
<td>9.98</td>
<td>9.60</td>
<td>9.36</td>
<td>9.20</td>
<td>9.07</td>
<td>8.98</td>
<td>8.90</td>
<td>8.84</td>
<td>8.75</td>
<td>8.66</td>
<td>8.56</td>
<td>8.51</td>
<td>8.46</td>
<td>8.41</td>
</tr>
<tr class="even">
<td>5</td>
<td>10.01</td>
<td>8.43</td>
<td>7.76</td>
<td>7.39</td>
<td>7.15</td>
<td>6.98</td>
<td>6.85</td>
<td>6.76</td>
<td>6.68</td>
<td>6.62</td>
<td>6.52</td>
<td>6.43</td>
<td>6.33</td>
<td>6.28</td>
<td>6.23</td>
<td>6.18</td>
</tr>
<tr class="odd">
<td>6</td>
<td>8.81</td>
<td>7.26</td>
<td>6.60</td>
<td>6.23</td>
<td>5.99</td>
<td>5.83</td>
<td>5.70</td>
<td>5.60</td>
<td>5.52</td>
<td>5.46</td>
<td>5.37</td>
<td>5.27</td>
<td>5.17</td>
<td>5.12</td>
<td>5.07</td>
<td>5.01</td>
</tr>
<tr class="even">
<td>7</td>
<td>8.07</td>
<td>6.54</td>
<td>5.89</td>
<td>5.52</td>
<td>5.29</td>
<td>5.12</td>
<td>4.99</td>
<td>4.90</td>
<td>4.82</td>
<td>4.76</td>
<td>4.67</td>
<td>4.57</td>
<td>4.47</td>
<td>4.42</td>
<td>4.36</td>
<td>4.31</td>
</tr>
<tr class="odd">
<td>8</td>
<td>7.57</td>
<td>6.06</td>
<td>5.42</td>
<td>5.05</td>
<td>4.82</td>
<td>4.65</td>
<td>4.53</td>
<td>4.43</td>
<td>4.36</td>
<td>4.30</td>
<td>4.20</td>
<td>4.10</td>
<td>4.00</td>
<td>3.95</td>
<td>3.89</td>
<td>3.84</td>
</tr>
<tr class="even">
<td>9</td>
<td>7.21</td>
<td>5.71</td>
<td>5.08</td>
<td>4.72</td>
<td>4.48</td>
<td>4.32</td>
<td>4.20</td>
<td>4.10</td>
<td>4.03</td>
<td>3.96</td>
<td>3.87</td>
<td>3.77</td>
<td>3.67</td>
<td>3.61</td>
<td>3.56</td>
<td>3.51</td>
</tr>
<tr class="odd">
<td>10</td>
<td>6.94</td>
<td>5.46</td>
<td>4.83</td>
<td>4.47</td>
<td>4.24</td>
<td>4.07</td>
<td>3.95</td>
<td>3.85</td>
<td>3.78</td>
<td>3.72</td>
<td>3.62</td>
<td>3.52</td>
<td>3.42</td>
<td>3.37</td>
<td>3.31</td>
<td>3.26</td>
</tr>
<tr class="even">
<td>11</td>
<td>6.72</td>
<td>5.26</td>
<td>4.63</td>
<td>4.28</td>
<td>4.04</td>
<td>3.88</td>
<td>3.76</td>
<td>3.66</td>
<td>3.59</td>
<td>3.53</td>
<td>3.43</td>
<td>3.33</td>
<td>3.23</td>
<td>3.17</td>
<td>3.12</td>
<td>3.06</td>
</tr>
<tr class="odd">
<td>12</td>
<td>6.55</td>
<td>5.10</td>
<td>4.47</td>
<td>4.12</td>
<td>3.89</td>
<td>3.73</td>
<td>3.61</td>
<td>3.51</td>
<td>3.44</td>
<td>3.37</td>
<td>3.28</td>
<td>3.18</td>
<td>3.07</td>
<td>3.02</td>
<td>2.96</td>
<td>2.91</td>
</tr>
<tr class="even">
<td>13</td>
<td>6.41</td>
<td>4.97</td>
<td>4.35</td>
<td>4.00</td>
<td>3.77</td>
<td>3.60</td>
<td>3.48</td>
<td>3.39</td>
<td>3.31</td>
<td>3.25</td>
<td>3.15</td>
<td>3.05</td>
<td>2.95</td>
<td>2.89</td>
<td>2.84</td>
<td>2.78</td>
</tr>
<tr class="odd">
<td>14</td>
<td>6.30</td>
<td>4.86</td>
<td>4.24</td>
<td>3.89</td>
<td>3.66</td>
<td>3.50</td>
<td>3.38</td>
<td>3.29</td>
<td>3.21</td>
<td>3.15</td>
<td>3.05</td>
<td>2.95</td>
<td>2.84</td>
<td>2.79</td>
<td>2.73</td>
<td>2.67</td>
</tr>
<tr class="even">
<td>15</td>
<td>6.20</td>
<td>4.77</td>
<td>4.15</td>
<td>3.80</td>
<td>3.58</td>
<td>3.41</td>
<td>3.29</td>
<td>3.20</td>
<td>3.12</td>
<td>3.06</td>
<td>2.96</td>
<td>2.86</td>
<td>2.76</td>
<td>2.70</td>
<td>2.64</td>
<td>2.59</td>
</tr>
<tr class="odd">
<td>16</td>
<td>6.12</td>
<td>4.69</td>
<td>4.08</td>
<td>3.73</td>
<td>3.50</td>
<td>3.34</td>
<td>3.22</td>
<td>3.12</td>
<td>3.05</td>
<td>2.99</td>
<td>2.89</td>
<td>2.79</td>
<td>2.68</td>
<td>2.63</td>
<td>2.57</td>
<td>2.51</td>
</tr>
<tr class="even">
<td>17</td>
<td>6.04</td>
<td>4.62</td>
<td>4.01</td>
<td>3.66</td>
<td>3.44</td>
<td>3.28</td>
<td>3.16</td>
<td>3.06</td>
<td>2.98</td>
<td>2.92</td>
<td>2.82</td>
<td>2.72</td>
<td>2.62</td>
<td>2.56</td>
<td>2.50</td>
<td>2.44</td>
</tr>
<tr class="odd">
<td>18</td>
<td>5.98</td>
<td>4.56</td>
<td>3.95</td>
<td>3.61</td>
<td>3.38</td>
<td>3.22</td>
<td>3.10</td>
<td>3.01</td>
<td>2.93</td>
<td>2.87</td>
<td>2.77</td>
<td>2.67</td>
<td>2.56</td>
<td>2.50</td>
<td>2.44</td>
<td>2.38</td>
</tr>
<tr class="even">
<td>19</td>
<td>5.92</td>
<td>4.51</td>
<td>3.90</td>
<td>3.56</td>
<td>3.33</td>
<td>3.17</td>
<td>3.05</td>
<td>2.96</td>
<td>2.88</td>
<td>2.82</td>
<td>2.72</td>
<td>2.62</td>
<td>2.51</td>
<td>2.45</td>
<td>2.39</td>
<td>2.33</td>
</tr>
<tr class="odd">
<td>20</td>
<td>5.87</td>
<td>4.46</td>
<td>3.86</td>
<td>3.51</td>
<td>3.29</td>
<td>3.13</td>
<td>3.01</td>
<td>2.91</td>
<td>2.84</td>
<td>2.77</td>
<td>2.68</td>
<td>2.57</td>
<td>2.46</td>
<td>2.41</td>
<td>2.35</td>
<td>2.29</td>
</tr>
<tr class="even">
<td>21</td>
<td>5.83</td>
<td>4.42</td>
<td>3.82</td>
<td>3.48</td>
<td>3.25</td>
<td>3.09</td>
<td>2.97</td>
<td>2.87</td>
<td>2.80</td>
<td>2.73</td>
<td>2.64</td>
<td>2.53</td>
<td>2.42</td>
<td>2.37</td>
<td>2.31</td>
<td>2.25</td>
</tr>
<tr class="odd">
<td>22</td>
<td>5.79</td>
<td>4.38</td>
<td>3.78</td>
<td>3.44</td>
<td>3.22</td>
<td>3.05</td>
<td>2.93</td>
<td>2.84</td>
<td>2.76</td>
<td>2.70</td>
<td>2.60</td>
<td>2.50</td>
<td>2.39</td>
<td>2.33</td>
<td>2.27</td>
<td>2.21</td>
</tr>
<tr class="even">
<td>23</td>
<td>5.75</td>
<td>4.35</td>
<td>3.75</td>
<td>3.41</td>
<td>3.18</td>
<td>3.02</td>
<td>2.90</td>
<td>2.81</td>
<td>2.73</td>
<td>2.67</td>
<td>2.57</td>
<td>2.47</td>
<td>2.36</td>
<td>2.30</td>
<td>2.24</td>
<td>2.18</td>
</tr>
<tr class="odd">
<td>24</td>
<td>5.72</td>
<td>4.32</td>
<td>3.72</td>
<td>3.38</td>
<td>3.15</td>
<td>2.99</td>
<td>2.87</td>
<td>2.78</td>
<td>2.70</td>
<td>2.64</td>
<td>2.54</td>
<td>2.44</td>
<td>2.33</td>
<td>2.27</td>
<td>2.21</td>
<td>2.15</td>
</tr>
<tr class="even">
<td>25</td>
<td>5.69</td>
<td>4.29</td>
<td>3.69</td>
<td>3.35</td>
<td>3.13</td>
<td>2.97</td>
<td>2.85</td>
<td>2.75</td>
<td>2.68</td>
<td>2.61</td>
<td>2.51</td>
<td>2.41</td>
<td>2.30</td>
<td>2.24</td>
<td>2.18</td>
<td>2.12</td>
</tr>
<tr class="odd">
<td>26</td>
<td>5.66</td>
<td>4.27</td>
<td>3.67</td>
<td>3.33</td>
<td>3.10</td>
<td>2.94</td>
<td>2.82</td>
<td>2.73</td>
<td>2.65</td>
<td>2.59</td>
<td>2.49</td>
<td>2.39</td>
<td>2.28</td>
<td>2.22</td>
<td>2.16</td>
<td>2.09</td>
</tr>
<tr class="even">
<td>27</td>
<td>5.63</td>
<td>4.24</td>
<td>3.65</td>
<td>3.31</td>
<td>3.08</td>
<td>2.92</td>
<td>2.80</td>
<td>2.71</td>
<td>2.63</td>
<td>2.57</td>
<td>2.47</td>
<td>2.36</td>
<td>2.25</td>
<td>2.19</td>
<td>2.13</td>
<td>2.07</td>
</tr>
<tr class="odd">
<td>28</td>
<td>5.61</td>
<td>4.22</td>
<td>3.63</td>
<td>3.29</td>
<td>3.06</td>
<td>2.90</td>
<td>2.78</td>
<td>2.69</td>
<td>2.61</td>
<td>2.55</td>
<td>2.45</td>
<td>2.34</td>
<td>2.23</td>
<td>2.17</td>
<td>2.11</td>
<td>2.05</td>
</tr>
<tr class="even">
<td>29</td>
<td>5.59</td>
<td>4.20</td>
<td>3.61</td>
<td>3.27</td>
<td>3.04</td>
<td>2.88</td>
<td>2.76</td>
<td>2.67</td>
<td>2.59</td>
<td>2.53</td>
<td>2.43</td>
<td>2.32</td>
<td>2.21</td>
<td>2.15</td>
<td>2.09</td>
<td>2.03</td>
</tr>
<tr class="odd">
<td>30</td>
<td>5.57</td>
<td>4.18</td>
<td>3.59</td>
<td>3.25</td>
<td>3.03</td>
<td>2.87</td>
<td>2.75</td>
<td>2.65</td>
<td>2.57</td>
<td>2.51</td>
<td>2.41</td>
<td>2.31</td>
<td>2.20</td>
<td>2.14</td>
<td>2.07</td>
<td>2.01</td>
</tr>
<tr class="even">
<td>40</td>
<td>5.42</td>
<td>4.05</td>
<td>3.46</td>
<td>3.13</td>
<td>2.90</td>
<td>2.74</td>
<td>2.62</td>
<td>2.53</td>
<td>2.45</td>
<td>2.39</td>
<td>2.29</td>
<td>2.18</td>
<td>2.07</td>
<td>2.01</td>
<td>1.94</td>
<td>1.88</td>
</tr>
<tr class="odd">
<td>60</td>
<td>5.29</td>
<td>3.93</td>
<td>3.34</td>
<td>3.01</td>
<td>2.79</td>
<td>2.63</td>
<td>2.51</td>
<td>2.41</td>
<td>2.33</td>
<td>2.27</td>
<td>2.17</td>
<td>2.06</td>
<td>1.94</td>
<td>1.88</td>
<td>1.82</td>
<td>1.74</td>
</tr>
<tr class="even">
<td>120</td>
<td>5.15</td>
<td>3.80</td>
<td>3.23</td>
<td>2.89</td>
<td>2.67</td>
<td>2.52</td>
<td>2.39</td>
<td>2.30</td>
<td>2.22</td>
<td>2.16</td>
<td>2.05</td>
<td>1.94</td>
<td>1.82</td>
<td>1.76</td>
<td>1.69</td>
<td>1.61</td>
</tr>
<tr class="odd">
<td>∞</td>
<td>5.02</td>
<td>3.69</td>
<td>3.12</td>
<td>2.79</td>
<td>2.57</td>
<td>2.41</td>
<td>2.29</td>
<td>2.19</td>
<td>2.11</td>
<td>2.05</td>
<td>1.94</td>
<td>1.83</td>
<td>1.71</td>
<td>1.64</td>
<td>1.57</td>
<td>1.48</td>
</tr>
</tbody>
</table>

For use for a one-tailed test of equality of standard deviation estimate
at 2.5 % level of confidence, or for a two-tailed test at 5 % level of
confidence.

**Table 9.5 Critical values for the F‑Test, F~0.99~**

> $\upsilon_{1}$ = degrees of freedom for numerator $\upsilon_{2}$ =
> degrees of freedom for denominator

<table>
<colgroup>
<col style="width: 6%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td><p><span class="math inline"><em>υ</em><sub>1</sub></span></p>
<p><span class="math inline"><em>υ</em><sub>2</sub></span></p></td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
<td>9</td>
<td>10</td>
</tr>
<tr class="even">
<td>10</td>
<td>10.04</td>
<td>7.56</td>
<td>6.55</td>
<td>5.99</td>
<td>5.64</td>
<td>5.39</td>
<td>5.20</td>
<td>5.06</td>
<td>4.94</td>
<td>4.85</td>
</tr>
<tr class="odd">
<td>11</td>
<td>9.65</td>
<td>7.21</td>
<td>6.22</td>
<td>5.67</td>
<td>5.32</td>
<td>5.07</td>
<td>4.89</td>
<td>4.74</td>
<td>4.63</td>
<td>4.54</td>
</tr>
<tr class="even">
<td>12</td>
<td>9.33</td>
<td>6.93</td>
<td>5.95</td>
<td>5.41</td>
<td>5.06</td>
<td>4.82</td>
<td>4.64</td>
<td>4.50</td>
<td>4.39</td>
<td>4.30</td>
</tr>
<tr class="odd">
<td>13</td>
<td>9.07</td>
<td>6.70</td>
<td>5.74</td>
<td>5.21</td>
<td>4.86</td>
<td>4.62</td>
<td>4.44</td>
<td>4.30</td>
<td>4.19</td>
<td>4.10</td>
</tr>
<tr class="even">
<td>14</td>
<td>8.86</td>
<td>6.51</td>
<td>5.56</td>
<td>5.04</td>
<td>4.69</td>
<td>4.46</td>
<td>4.28</td>
<td>4.14</td>
<td>4.03</td>
<td>3.94</td>
</tr>
<tr class="odd">
<td>15</td>
<td>8.68</td>
<td>6.36</td>
<td>5.42</td>
<td>4.89</td>
<td>4.56</td>
<td>4.32</td>
<td>4.14</td>
<td>4.00</td>
<td>3.89</td>
<td>3.80</td>
</tr>
<tr class="even">
<td>16</td>
<td>8.53</td>
<td>6.23</td>
<td>5.29</td>
<td>4.77</td>
<td>4.44</td>
<td>4.20</td>
<td>4.03</td>
<td>3.89</td>
<td>3.78</td>
<td>3.69</td>
</tr>
<tr class="odd">
<td>17</td>
<td>8.40</td>
<td>6.11</td>
<td>5.18</td>
<td>4.67</td>
<td>4.34</td>
<td>4.10</td>
<td>3.93</td>
<td>3.79</td>
<td>3.68</td>
<td>3.59</td>
</tr>
<tr class="even">
<td>18</td>
<td>8.29</td>
<td>6.01</td>
<td>5.09</td>
<td>4.58</td>
<td>4.25</td>
<td>4.01</td>
<td>3.84</td>
<td>3.71</td>
<td>3.60</td>
<td>3.51</td>
</tr>
<tr class="odd">
<td>19</td>
<td>8.18</td>
<td>5.93</td>
<td>5.01</td>
<td>4.50</td>
<td>4.17</td>
<td>3.94</td>
<td>3.77</td>
<td>3.63</td>
<td>3.52</td>
<td>3.43</td>
</tr>
<tr class="even">
<td>20</td>
<td>8.10</td>
<td>5.85</td>
<td>4.94</td>
<td>4.43</td>
<td>4.10</td>
<td>3.87</td>
<td>3.70</td>
<td>3.56</td>
<td>3.46</td>
<td>3.37</td>
</tr>
<tr class="odd">
<td>22</td>
<td>7.95</td>
<td>5.72</td>
<td>4.82</td>
<td>4.31</td>
<td>3.99</td>
<td>3.76</td>
<td>3.59</td>
<td>3.45</td>
<td>3.35</td>
<td>3.26</td>
</tr>
<tr class="even">
<td>24</td>
<td>7.82</td>
<td>5.61</td>
<td>4.72</td>
<td>4.22</td>
<td>3.90</td>
<td>3.67</td>
<td>3.50</td>
<td>3.36</td>
<td>3.26</td>
<td>3.17</td>
</tr>
<tr class="odd">
<td>26</td>
<td>7.72</td>
<td>5.53</td>
<td>4.64</td>
<td>4.14</td>
<td>3.82</td>
<td>3.59</td>
<td>3.42</td>
<td>3.29</td>
<td>3.18</td>
<td>3.09</td>
</tr>
<tr class="even">
<td>28</td>
<td>7.64</td>
<td>5.45</td>
<td>4.57</td>
<td>4.07</td>
<td>3.75</td>
<td>3.53</td>
<td>3.36</td>
<td>3.23</td>
<td>3.12</td>
<td>3.03</td>
</tr>
<tr class="odd">
<td>30</td>
<td>7.56</td>
<td>5.39</td>
<td>4.51</td>
<td>4.02</td>
<td>3.70</td>
<td>3.47</td>
<td>3.30</td>
<td>3.17</td>
<td>3.07</td>
<td>2.98</td>
</tr>
<tr class="even">
<td>35</td>
<td>7.42</td>
<td>5.27</td>
<td>4.40</td>
<td>3.91</td>
<td>3.59</td>
<td>3.37</td>
<td>3.20</td>
<td>3.07</td>
<td>2.96</td>
<td>2.88</td>
</tr>
<tr class="odd">
<td>40</td>
<td>7.31</td>
<td>5.18</td>
<td>4.31</td>
<td>3.83</td>
<td>3.51</td>
<td>3.29</td>
<td>3.12</td>
<td>2.99</td>
<td>2.89</td>
<td>2.80</td>
</tr>
<tr class="even">
<td>45</td>
<td>7.23</td>
<td>5.11</td>
<td>4.25</td>
<td>3.77</td>
<td>3.45</td>
<td>3.23</td>
<td>3.07</td>
<td>2.94</td>
<td>2.83</td>
<td>2.74</td>
</tr>
<tr class="odd">
<td>50</td>
<td>7.17</td>
<td>5.06</td>
<td>4.20</td>
<td>3.72</td>
<td>3.41</td>
<td>3.19</td>
<td>3.02</td>
<td>2.89</td>
<td>2.78</td>
<td>2.70</td>
</tr>
<tr class="even">
<td>55</td>
<td>7.12</td>
<td>5.01</td>
<td>4.16</td>
<td>3.68</td>
<td>3.37</td>
<td>3.15</td>
<td>2.98</td>
<td>2.85</td>
<td>2.75</td>
<td>2.66</td>
</tr>
<tr class="odd">
<td>60</td>
<td>7.08</td>
<td>4.98</td>
<td>4.13</td>
<td>3.65</td>
<td>3.34</td>
<td>3.12</td>
<td>2.95</td>
<td>2.82</td>
<td>2.72</td>
<td>2.63</td>
</tr>
<tr class="even">
<td>65</td>
<td>7.04</td>
<td>4.95</td>
<td>4.10</td>
<td>3.62</td>
<td>3.31</td>
<td>3.09</td>
<td>2.93</td>
<td>2.80</td>
<td>2.69</td>
<td>2.61</td>
</tr>
<tr class="odd">
<td>70</td>
<td>7.01</td>
<td>4.92</td>
<td>4.07</td>
<td>3.60</td>
<td>3.29</td>
<td>3.07</td>
<td>2.91</td>
<td>2.78</td>
<td>2.67</td>
<td>2.59</td>
</tr>
<tr class="even">
<td>75</td>
<td>6.99</td>
<td>4.90</td>
<td>4.05</td>
<td>3.58</td>
<td>3.27</td>
<td>3.05</td>
<td>2.89</td>
<td>2.76</td>
<td>2.65</td>
<td>2.57</td>
</tr>
<tr class="odd">
<td>80</td>
<td>6.96</td>
<td>4.88</td>
<td>4.04</td>
<td>3.56</td>
<td>3.25</td>
<td>3.04</td>
<td>2.87</td>
<td>2.74</td>
<td>2.64</td>
<td>2.55</td>
</tr>
<tr class="even">
<td>85</td>
<td>6.94</td>
<td>4.86</td>
<td>4.02</td>
<td>3.55</td>
<td>3.24</td>
<td>3.02</td>
<td>2.86</td>
<td>2.73</td>
<td>2.62</td>
<td>2.54</td>
</tr>
<tr class="odd">
<td>90</td>
<td>6.93</td>
<td>4.85</td>
<td>4.01</td>
<td>3.53</td>
<td>3.23</td>
<td>3.01</td>
<td>2.84</td>
<td>2.72</td>
<td>2.61</td>
<td>2.52</td>
</tr>
<tr class="even">
<td>95</td>
<td>6.91</td>
<td>4.84</td>
<td>3.99</td>
<td>3.52</td>
<td>3.22</td>
<td>3.00</td>
<td>2.83</td>
<td>2.70</td>
<td>2.60</td>
<td>2.51</td>
</tr>
<tr class="odd">
<td>100</td>
<td>6.90</td>
<td>4.82</td>
<td>3.98</td>
<td>3.51</td>
<td>3.21</td>
<td>2.99</td>
<td>2.82</td>
<td>2.69</td>
<td>2.59</td>
<td>2.50</td>
</tr>
<tr class="even">
<td>105</td>
<td>6.88</td>
<td>4.81</td>
<td>3.97</td>
<td>3.50</td>
<td>3.20</td>
<td>2.98</td>
<td>2.81</td>
<td>2.69</td>
<td>2.58</td>
<td>2.49</td>
</tr>
<tr class="odd">
<td>110</td>
<td>6.87</td>
<td>4.80</td>
<td>3.96</td>
<td>3.49</td>
<td>3.19</td>
<td>2.97</td>
<td>2.81</td>
<td>2.68</td>
<td>2.57</td>
<td>2.49</td>
</tr>
<tr class="even">
<td>115</td>
<td>6.86</td>
<td>4.79</td>
<td>3.96</td>
<td>3.49</td>
<td>3.18</td>
<td>2.96</td>
<td>2.80</td>
<td>2.67</td>
<td>2.57</td>
<td>2.48</td>
</tr>
<tr class="odd">
<td>120</td>
<td>6.85</td>
<td>4.79</td>
<td>3.95</td>
<td>3.48</td>
<td>3.17</td>
<td>2.96</td>
<td>2.79</td>
<td>2.66</td>
<td>2.56</td>
<td>2.47</td>
</tr>
<tr class="even">
<td>∞</td>
<td>6.63</td>
<td>4.61</td>
<td>3.78</td>
<td>3.32</td>
<td>3.02</td>
<td>2.80</td>
<td>2.64</td>
<td>2.51</td>
<td>2.41</td>
<td>2.32</td>
</tr>
</tbody>
</table>

For use for a one-tailed test of equality of standard deviation estimate
at 2.5 % level of confidence, or for a two-tailed test at 2 % level of
confidence.

**Table 9.6 Factors for Two‑sided Tolerance Intervals**

**for the Normal Distribution**

<table style="width:100%;">
<colgroup>
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td colspan="5"><span class="math inline"><em>γ</em></span> = 0.95</td>
<td colspan="5"><span class="math inline"><em>γ</em></span> = 0.99</td>
</tr>
<tr class="even">
<td><p>P</p>
<p>n</p></td>
<td>0.75</td>
<td>0.90</td>
<td>0.95</td>
<td>0.99</td>
<td>0.999</td>
<td>0.75</td>
<td>0.90</td>
<td>0.95</td>
<td>0.99</td>
<td>0.999</td>
</tr>
<tr class="odd">
<td>2</td>
<td>22.858</td>
<td>32.019</td>
<td>37.674</td>
<td>48.430</td>
<td>60.573</td>
<td>114.363</td>
<td>160.193</td>
<td>188.491</td>
<td>242.300</td>
<td>303.054</td>
</tr>
<tr class="even">
<td>3</td>
<td>5.922</td>
<td>8.380</td>
<td>9.916</td>
<td>12.861</td>
<td>16.208</td>
<td>13.378</td>
<td>18.930</td>
<td>22.401</td>
<td>29.055</td>
<td>36.616</td>
</tr>
<tr class="odd">
<td>4</td>
<td>3.779</td>
<td>5.369</td>
<td>6.370</td>
<td>8.299</td>
<td>10.502</td>
<td>6.614</td>
<td>9.398</td>
<td>11.150</td>
<td>14.527</td>
<td>18.383</td>
</tr>
<tr class="even">
<td>5</td>
<td>3.002</td>
<td>4.275</td>
<td>5.079</td>
<td>6.634</td>
<td>8.415</td>
<td>4.643</td>
<td>6.612</td>
<td>7.855</td>
<td>10.260</td>
<td>13.015</td>
</tr>
<tr class="odd">
<td>6</td>
<td>2.604</td>
<td>3.712</td>
<td>4.414</td>
<td>5.775</td>
<td>7.337</td>
<td>3.743</td>
<td>5.337</td>
<td>6.345</td>
<td>8.301</td>
<td>10.548</td>
</tr>
<tr class="even">
<td>7</td>
<td>2.361</td>
<td>3.369</td>
<td>4.007</td>
<td>5.248</td>
<td>6.676</td>
<td>3.233</td>
<td>4.613</td>
<td>5.488</td>
<td>7.187</td>
<td>9.142</td>
</tr>
<tr class="odd">
<td>8</td>
<td>2.197</td>
<td>3.136</td>
<td>3.732</td>
<td>4.891</td>
<td>6.226</td>
<td>2.905</td>
<td>4.147</td>
<td>4.936</td>
<td>6.468</td>
<td>8.234</td>
</tr>
<tr class="even">
<td>9</td>
<td>2.078</td>
<td>2.967</td>
<td>3.532</td>
<td>4.631</td>
<td>5.899</td>
<td>2.677</td>
<td>3.822</td>
<td>4.550</td>
<td>5.966</td>
<td>7.600</td>
</tr>
<tr class="odd">
<td>10</td>
<td>1.987</td>
<td>2.839</td>
<td>3.379</td>
<td>4.433</td>
<td>5.649</td>
<td>2.508</td>
<td>3.582</td>
<td>4.265</td>
<td>5.594</td>
<td>7.129</td>
</tr>
<tr class="even">
<td>11</td>
<td>1.916</td>
<td>2.737</td>
<td>3.259</td>
<td>4.277</td>
<td>5.452</td>
<td>2.378</td>
<td>3.397</td>
<td>4.045</td>
<td>5.308</td>
<td>6.766</td>
</tr>
<tr class="odd">
<td>12</td>
<td>1.858</td>
<td>2.655</td>
<td>3.162</td>
<td>4.150</td>
<td>5.291</td>
<td>2.274</td>
<td>3.250</td>
<td>3.870</td>
<td>5.079</td>
<td>6.477</td>
</tr>
<tr class="even">
<td>13</td>
<td>1.810</td>
<td>2.587</td>
<td>3.081</td>
<td>4.044</td>
<td>5.158</td>
<td>2.190</td>
<td>3.130</td>
<td>3.727</td>
<td>4.893</td>
<td>6.240</td>
</tr>
<tr class="odd">
<td>14</td>
<td>1.770</td>
<td>2.529</td>
<td>3.012</td>
<td>3.955</td>
<td>5.045</td>
<td>2.120</td>
<td>3.029</td>
<td>3.608</td>
<td>4.737</td>
<td>6.043</td>
</tr>
<tr class="even">
<td>15</td>
<td>1.735</td>
<td>2.480</td>
<td>2.954</td>
<td>3.878</td>
<td>4.949</td>
<td>2.060</td>
<td>2.945</td>
<td>3.507</td>
<td>4.605</td>
<td>5.876</td>
</tr>
<tr class="odd">
<td>16</td>
<td>1.705</td>
<td>2.437</td>
<td>2.903</td>
<td>3.812</td>
<td>4.865</td>
<td>2.009</td>
<td>2.872</td>
<td>3.421</td>
<td>4.492</td>
<td>5.732</td>
</tr>
<tr class="even">
<td>17</td>
<td>1.679</td>
<td>2.400</td>
<td>2.858</td>
<td>3.754</td>
<td>4.791</td>
<td>1.965</td>
<td>2.808</td>
<td>3.345</td>
<td>4.393</td>
<td>5.607</td>
</tr>
<tr class="odd">
<td>18</td>
<td>1.655</td>
<td>2.366</td>
<td>2.819</td>
<td>3.702</td>
<td>4.725</td>
<td>1.926</td>
<td>2.753</td>
<td>3.279</td>
<td>4.307</td>
<td>5.497</td>
</tr>
<tr class="even">
<td>19</td>
<td>1.635</td>
<td>2.337</td>
<td>2.784</td>
<td>3.656</td>
<td>4.667</td>
<td>1.891</td>
<td>2.703</td>
<td>3.221</td>
<td>4.230</td>
<td>5.399</td>
</tr>
<tr class="odd">
<td>20</td>
<td>1.616</td>
<td>2.310</td>
<td>2.752</td>
<td>3.612</td>
<td>4.614</td>
<td>1.860</td>
<td>2.659</td>
<td>3.168</td>
<td>4.161</td>
<td>5.312</td>
</tr>
<tr class="even">
<td>21</td>
<td>1.599</td>
<td>2.286</td>
<td>2.723</td>
<td>3.577</td>
<td>4.567</td>
<td>1.833</td>
<td>2.620</td>
<td>3.121</td>
<td>4.100</td>
<td>5.234</td>
</tr>
<tr class="odd">
<td>22</td>
<td>1.584</td>
<td>2.264</td>
<td>2.697</td>
<td>3.543</td>
<td>4.523</td>
<td>1.808</td>
<td>2.584</td>
<td>3.078</td>
<td>4.044</td>
<td>5.163</td>
</tr>
<tr class="even">
<td>23</td>
<td>1.570</td>
<td>2.244</td>
<td>2.673</td>
<td>3.512</td>
<td>4.484</td>
<td>1.785</td>
<td>2.551</td>
<td>3.040</td>
<td>3.993</td>
<td>5.098</td>
</tr>
<tr class="odd">
<td>24</td>
<td>1.557</td>
<td>2.225</td>
<td>2.651</td>
<td>3.483</td>
<td>4.447</td>
<td>1.764</td>
<td>2.522</td>
<td>3.004</td>
<td>3.947</td>
<td>5.039</td>
</tr>
<tr class="even">
<td>25</td>
<td>1.545</td>
<td>2.208</td>
<td>2.631</td>
<td>3.457</td>
<td>4.413</td>
<td>1.745</td>
<td>2.494</td>
<td>2.972</td>
<td>3.904</td>
<td>4.985</td>
</tr>
<tr class="odd">
<td>26</td>
<td>1.534</td>
<td>2.193</td>
<td>2.612</td>
<td>3.432</td>
<td>4.382</td>
<td>1.727</td>
<td>2.469</td>
<td>2.941</td>
<td>3.865</td>
<td>4.935</td>
</tr>
<tr class="even">
<td>27</td>
<td>1.523</td>
<td>2.178</td>
<td>2.595</td>
<td>3.409</td>
<td>4.353</td>
<td>1.711</td>
<td>2.446</td>
<td>2.914</td>
<td>3.828</td>
<td>4.888</td>
</tr>
</tbody>
</table>

From: NBS Handbook 91, p T‑11

**Table 9.7 Factors for Computing Two‑sided Confidence Limits for α
(Part 1)**

+-------+---------+---------+---------+---------+---------+---------+
| **De  | α =     |         | α **=   |         | α **=   |         |
| grees | 0.05    |         | 0.01**  |         | 0.001** |         |
| of**  |         |         |         |         |         |         |
|       |         |         |         |         |         |         |
| *     |         |         |         |         |         |         |
| *Free |         |         |         |         |         |         |
| dom** |         |         |         |         |         |         |
+-------+---------+---------+---------+---------+---------+---------+
|       | *       | *       | *       | *       | *       | *       |
|       | *S~U~** | *S~L~** | *S~U~** | *S~L~** | *S~U~** | *S~L~** |
+-------+---------+---------+---------+---------+---------+---------+
| 1     | 17.79   | 0.3576  | 86.31   | 0.2969  | 844.4   | 0.2480  |
+-------+---------+---------+---------+---------+---------+---------+
| 2     | 4.859   | 0.4581  | 10.70   | 0.3879  | 33.29   | 0.3291  |
+-------+---------+---------+---------+---------+---------+---------+
| 3     | 3.183   | 0.5178  | 5.449   | 0.4453  | 11.65   | 0.3824  |
+-------+---------+---------+---------+---------+---------+---------+
| 4     | 2.567   | 0.5590  | 3.892   | 0.4865  | 6.938   | 0.4218  |
+-------+---------+---------+---------+---------+---------+---------+
| 5     | 2.248   | 0.5899  | 3.175   | 0.5182  | 5.085   | 0.4529  |
+-------+---------+---------+---------+---------+---------+---------+
| 6     | 2.052   | 0.6143  | 2.764   | 0.5437  | 4.128   | 0.4784  |
+-------+---------+---------+---------+---------+---------+---------+
| 7     | 1.918   | 0.6344  | 2.498   | 0.5650  | 3.551   | 0.5000  |
+-------+---------+---------+---------+---------+---------+---------+
| 8     | 1.820   | 0.6513  | 2.311   | 0.5830  | 3.167   | 0.5186  |
+-------+---------+---------+---------+---------+---------+---------+
| 9     | 1.746   | 0.6657  | 2.173   | 0.5987  | 2.894   | 0.5348  |
+-------+---------+---------+---------+---------+---------+---------+
| 10    | 1.686   | 0.6784  | 2.065   | 0.6125  | 2.689   | 0.5492  |
+-------+---------+---------+---------+---------+---------+---------+
| 11    | 1.638   | 0.6896  | 1.980   | 0.6248  | 2.530   | 0.5621  |
+-------+---------+---------+---------+---------+---------+---------+
| 12    | 1.598   | 0.6995  | 1.909   | 0.6358  | 2.402   | 0.5738  |
+-------+---------+---------+---------+---------+---------+---------+
| 13    | 1.564   | 0.7084  | 1.851   | 0.6458  | 2.298   | 0.5845  |
+-------+---------+---------+---------+---------+---------+---------+
| 14    | 1.534   | 0.7166  | 1.801   | 0.6549  | 2.210   | 0.5942  |
+-------+---------+---------+---------+---------+---------+---------+
| 15    | 1.509   | 0.7240  | 1.758   | 0.6632  | 2.136   | 0.6032  |
+-------+---------+---------+---------+---------+---------+---------+
| 16    | 1.486   | 0.7808  | 1.721   | 0.6710  | 2.073   | 0.6116  |
+-------+---------+---------+---------+---------+---------+---------+
| 17    | 1.466   | 0.7372  | 1.688   | 0.6781  | 2.017   | 0.6193  |
+-------+---------+---------+---------+---------+---------+---------+
| 18    | 1.448   | 0.7430  | 1.658   | 0.6848  | 1.968   | 0.6266  |
+-------+---------+---------+---------+---------+---------+---------+
| 19    | 1.432   | 0.7484  | 1.632   | 0.6909  | 1.925   | 0.6333  |
+-------+---------+---------+---------+---------+---------+---------+
| 20    | 1.417   | 0.7535  | 1.609   | 0.6968  | 1.886   | 0.6397  |
+-------+---------+---------+---------+---------+---------+---------+
| 21    | 1.404   | 0.7582  | 1.587   | 0.7022  | 1.851   | 0.6457  |
+-------+---------+---------+---------+---------+---------+---------+
| 22    | 1.391   | 0.7627  | 1.568   | 0.7074  | 1.820   | 0.6514  |
+-------+---------+---------+---------+---------+---------+---------+
| 23    | 1.380   | 0.7669  | 1.550   | 0.7122  | 1.791   | 0.6568  |
+-------+---------+---------+---------+---------+---------+---------+
| 24    | 1.370   | 0.7709  | 1.533   | 0.7169  | 1.765   | 0.6619  |
+-------+---------+---------+---------+---------+---------+---------+
| 25    | 1.360   | 0.7747  | 1.518   | 0.7212  | 1.741   | 0.6668  |
+-------+---------+---------+---------+---------+---------+---------+

From: NBS Handbook 91, p T‑34

**Table 9.7 Factors for Computing Two‑sided Confidence Limits for α
(Part 2)**

+-------+---------+---------+---------+---------+---------+---------+
| **De  | α **=   |         | α **=   |         | α **=   |         |
| grees | 0.05**  |         | 0.01**  |         | 0.001** |         |
| of**  |         |         |         |         |         |         |
|       |         |         |         |         |         |         |
| Fr    |         |         |         |         |         |         |
| eedom |         |         |         |         |         |         |
+-------+---------+---------+---------+---------+---------+---------+
|       | *       | *       | *       | *       | *       | *       |
|       | *S~U~** | *S~L~** | *S~U~** | *S~L~** | *S~U~** | *S~L~** |
+-------+---------+---------+---------+---------+---------+---------+
| 26    | 1.351   | 0.7783  | 1.504   | 0.7253  | 1.719   | 0.7130  |
+-------+---------+---------+---------+---------+---------+---------+
| 27    | 1.343   | 0.7817  | 1.491   | 0.7293  | 1.698   | 0.6758  |
+-------+---------+---------+---------+---------+---------+---------+
| 28    | 1.335   | 0.7849  | 1.479   | 0.7331  | 1.679   | 0.6800  |
+-------+---------+---------+---------+---------+---------+---------+
| 29    | 1.327   | 0.7880  | 1.467   | 0.7367  | 1.661   | 0.6841  |
+-------+---------+---------+---------+---------+---------+---------+
| 30    | 1.321   | 0.7909  | 1.457   | 0.7401  | 1.645   | 0.6880  |
+-------+---------+---------+---------+---------+---------+---------+
| 31    | 1.314   | 0.7937  | 1.447   | 0.7434  | 1.629   | 0.6917  |
+-------+---------+---------+---------+---------+---------+---------+
| 32    | 1.308   | 0.7964  | 1.437   | 0.7467  | 1.615   | 0.6953  |
+-------+---------+---------+---------+---------+---------+---------+
| 33    | 1.302   | 0.7990  | 1.428   | 0.7497  | 1.601   | 0.6987  |
+-------+---------+---------+---------+---------+---------+---------+
| 34    | 1.296   | 0.8015  | 1.420   | 0.7526  | 1.588   | 0.7020  |
+-------+---------+---------+---------+---------+---------+---------+
| 35    | 1.291   | 0.8089  | 1.412   | 0.7554  | 1.576   | 0.7052  |
+-------+---------+---------+---------+---------+---------+---------+
| 36    | 1.286   | 0.8062  | 1.404   | 0.7582  | 1.564   | 0.7083  |
+-------+---------+---------+---------+---------+---------+---------+
| 37    | 1.281   | 0.8085  | 1.397   | 0.7608  | 1.553   | 0.7113  |
+-------+---------+---------+---------+---------+---------+---------+
| 38    | 1.277   | 0.8106  | 1.390   | 0.7633  | 1.543   | 0.7141  |
+-------+---------+---------+---------+---------+---------+---------+
| 39    | 1.272   | 0.8126  | 1.383   | 0.7658  | 1.533   | 0.7169  |
+-------+---------+---------+---------+---------+---------+---------+
| 40    | 1.268   | 0.8146  | 1.377   | 0.7681  | 1.523   | 0.7197  |
+-------+---------+---------+---------+---------+---------+---------+
| 41    | 1.264   | 0.8166  | 1.371   | 0.7705  | 1.515   | 0.7223  |
+-------+---------+---------+---------+---------+---------+---------+
| 42    | 1.260   | 0.8184  | 1.365   | 0.7727  | 1.506   | 0.7248  |
+-------+---------+---------+---------+---------+---------+---------+
| 43    | 1.257   | 0.8202  | 1.360   | 0.7748  | 1.498   | 0.7273  |
+-------+---------+---------+---------+---------+---------+---------+
| 44    | 1.253   | 0.8220  | 1.355   | 0.7769  | 1.490   | 0.7297  |
+-------+---------+---------+---------+---------+---------+---------+
| 45    | 1.249   | 0.8237  | 1.349   | 0.7789  | 1.482   | 0.7320  |
+-------+---------+---------+---------+---------+---------+---------+
| 46    | 1.246   | 0.8253  | 1.345   | 0.7809  | 1.475   | 0.7342  |
+-------+---------+---------+---------+---------+---------+---------+
| 47    | 1.243   | 0.8269  | 1.340   | 0.7828  | 1.468   | 0.7364  |
+-------+---------+---------+---------+---------+---------+---------+
| 48    | 1.240   | 0.8285  | 1.335   | 0.7847  | 1.462   | 0.7386  |
+-------+---------+---------+---------+---------+---------+---------+
| 49    | 1.237   | 0.8300  | 1.331   | 0.7864  | 1.455   | 0.7407  |
+-------+---------+---------+---------+---------+---------+---------+
| 50    | 1.234   | 0.8314  | 1.327   | 0.7882  | 1.449   | 0.7427  |
+-------+---------+---------+---------+---------+---------+---------+

From: NBS Handbook 91, p. T-34

**Table 9.8 Density of Air‑free Water in g/cm^3^ as a**

**Function of Celsius Temperature**

  ------ ------- ------- ------- ------- ------- ------- ------- ------- ------- -------
  T      **0.0   **0.1   **0.2   **0.3   **0.4   **0.5   **0.6   **0.7   **0.8   **0.9
         °C**    °C**    °C**    °C**    °C**    °C**    °C**    °C**    °C**    °C**

  0.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         840     846     853     859     865     871     877     883     888     893

  1.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         899     903     908     913     917     921     925     929     933     937

  2.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         940     943     946     949     952     954     956     959     961     963

  3.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         964     966     967     968     969     970     971     971     972     972

  4.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         972     972     972     971     971     970     969     968     967     965

  5.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         964     962     960     958     956     954     951     949     946     943

  6.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         940     937     933     930     926     922     918     914     910     906

  7.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         901     896     892     887     881     876     871     865     860     854

  8.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         848     842     835     829     822     816     809     802     795     787

  9.0    0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         780     773     765     757     749     741     733     725     716     707

  10.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         699     690     681     672     662     653     643     634     624     614

  11.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         604     594     583     573     562     552     541     530     519     507

  12.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         496     485     473     461     449     437     425     413     401     388

  13.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         376     363     350     337     324     311     297     284     270     256

  14.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.999
         243     229     215     200     186     172     157     142     128     113

  15.0   0.999   0.999   0.999   0.999   0.999   0.999   0.999   0.998   0.998   0.998
         098     083     067     052     036     021     005     989     973     957

  16.0   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998
         941     925     908     892     875     858     841     824     807     790

  17.0   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998
         773     755     738     720     702     684     666     648     630     612

  18.0   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998
         593     575     556     537     519     500     480     461     442     422

  19.0   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998
         403     383     364     344     324     304     284     263     243     222

  20.0   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998   0.998
         202     181     160     139     118     097     076     055     033     012

  21.0   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997
         990     968     947     925     903     881     858     836     814     791

  22.0   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997
         768     746     723     700     677     654     630     607     584     560

  23.0   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997
         536     513     489     465     441     417     392     368     344     319

  24.0   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997   0.997
         294     270     245     220     195     170     145     119     094     068

  25.0   0.997   0.997   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996
         043     017     991     966     940     913     887     861     835     808

  26.0   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996
         782     755     728     702     675     648     621     593     566     539

  27.0   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996
         511     484     456     428     401     373     345     316     288     260

  28.0   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.996   0.995
         232     203     175     146     117     088     060     031     001     972

  29.0   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995
         943     914     884     855     825     795     765     736     706     676

  30.0   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995
         645     615     585     554     524     493     463     432     401     370

  31.0   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995   0.995
         339     308     277     246     214     183     151     120     088     056

  32.0   0.995   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994
         024     992     960     928     896     864     831     799     766     734

  33.0   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994
         701     668     635     602     569     536     503     470     436     403

  34.0   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994   0.994
         369     336     302     268     234     201     167     132     098     064

  35.0   0.994   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993
         030     995     961     926     891     857     822     787     752     717

  36.0   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993
         682     647     611     576     541     505     469     434     398     362

  37.0   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993   0.993
         326     290     254     218     182     146     109     073     036     000

  38.0   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992
         963     926     889     852     815     778     741     704     667     629

  39.0   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992   0.992
         592     554     517     479     442     404     366     328     290     252
  ------ ------- ------- ------- ------- ------- ------- ------- ------- ------- -------

\*Based on the work of H. Wagenbreth and W. Blanke, PTB ‑ Mitteilingen
6‑71.

Reference equations for Air-Saturated or Air-Free distilled water may be
used but reference source should be noted.

**Table 9.9 Density of Air, g/cm^3^, as Function of Temperature and Air
Pressure^\*^**

  -------------- ---------- ------- ---------------- -------- -------- -------- -------- --------
  **Barometric                      **Temperature,                                       
  Pressure**                        °C**                                                 

  **kPa**        **mbar**   **mm    **18**           **20**   **22**   **24**   **26**   **28**
                            Hg**                                                         

  77.33          773        580     0.000 92         0.000 92 0.000 91 0.000 91 0.000 90 0.000 90

  79.99          800        600     0.000 95         0.000 95 0.000 94 0.000 93 0.000 93 0.000 92

  82.66          827        620     0.000 99         0.000 98 0.000 97 0.000 96 0.000 96 0.000 95

  85.33          853        640     0.001 02         0.001 01 0.001 00 0.001 00 0.000 99 0.000 98

  87.99          880        660     0.001 05         0.001 04 0.001 03 0.001 03 0.001 02 0.001 01

  90.66          907        680     0.001 08         0.001 07 0.001 07 0.001 06 0.001 05 0.001 04

  93.33          933        700     0.001 11         0.001 10 0.001 10 0.001 09 0.001 08 0.001 07

  95.99          960        720     0.001 14         0.001 14 0.001 13 0.001 12 0.001 12 0.001 10

  98.66          987        740     0.001 18         0.001 17 0.001 16 0.001 15 0.001 14 0.001 13

  101.32         1013       760     0.001 21         0.001 20 0.001 19 0.001 18 0.001 17 0.001 17

  103.99         1040       780     0.001 24         0.001 23 0.001 22 0.001 21 0.001 21 0.001 20

  106.66         1067       800     0.001 27         0.001 26 0.001 25 0.001 24 0.001 24 0.001 23
  -------------- ---------- ------- ---------------- -------- -------- -------- -------- --------

Computed for air at 50 % relative humidity

\*Equations to compute the density of air at any pressure, temperature,
and relative humidity are given in Section 8 of the Appendix to SOP No.
2 and are preferred for all precision mass and volume calibrations.

**Table 9.10 Density and Coefficient of Expansion**

+----------------+------------+------------+------------+------------+
| #              | ## *       | **C        |            |            |
| # **Material** | *Density** | oefficient |            |            |
|                |            | of         |            |            |
|                |            | E          |            |            |
|                |            | xpansion** |            |            |
+----------------+------------+------------+------------+------------+
|                | > *        | **Linear   | **Cubical  | **Cubical  |
|                | *g/cm^3^** | (/°C)**    | (/°C)**    | (/°F)**    |
+----------------+------------+------------+------------+------------+
| > Aluminum     | > 2.7      | > 0.000    | > 0.000    | > 0.000    |
|                |            | > 024      | > 069      | > 038      |
|                |            |            |            | >          |
|                |            |            |            | > *(not    |
|                |            |            |            | > suitable |
|                |            |            |            | > for      |
|                |            |            |            | >          |
|                |            |            |            |  provers)* |
+----------------+------------+------------+------------+------------+
| ## Brass       | > 8.4 at 0 | > 0.000    | > 0.000    |            |
|                | > °C       | > 019      | > 054      |            |
|                |            |            |            |            |
|                | ## 8.390   |            |            |            |
|                | 9 at 20 °C |            |            |            |
+----------------+------------+------------+------------+------------+
| > Cast iron    | > 7.0      | > 0.000    | > 0.000    |            |
|                | >          | > 010      | > 030      |            |
|                | > 7.2      |            |            |            |
+----------------+------------+------------+------------+------------+
| > Copper       |            | > 0.000    | > 0.000    |            |
|                |            | > 017      | > 050      |            |
+----------------+------------+------------+------------+------------+
| > Diamond      |            | > 0.000    | > 0.000    |            |
|                |            | > 001 18   | > 003 5    |            |
+----------------+------------+------------+------------+------------+
| > Fused silica |            | > 0.000    | > 0.000    |            |
| > (quartz)     |            | > 000 5    | > 001 6    |            |
+----------------+------------+------------+------------+------------+
| > Glass,       |            |            | > 0.000    |            |
| > borosilicate |            |            | > 010      |            |
| > (T1CA)       |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Glass,       |            |            | > 0.000    |            |
| > borosilicate |            |            | > 015      |            |
| > (T1CB)       |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Glass,       |            |            | > 0.000    |            |
| > soda-lime    |            |            | > 025      |            |
+----------------+------------+------------+------------+------------+
| > Gold         | > 18.0     |            | > 0.000    |            |
|                |            |            | > 043      |            |
+----------------+------------+------------+------------+------------+
| > Invar        |            | > 0.000    | > 0.000    |            |
|                |            | > 000 4    | > 001 2    |            |
+----------------+------------+------------+------------+------------+
| > Lead         | > 11.34    | > 0.000    | > 0.000    |            |
|                |            | > 029      | > 087      |            |
+----------------+------------+------------+------------+------------+
| > Length bench |            | > 0.000    |            |            |
|                |            | > 010 6    |            |            |
+----------------+------------+------------+------------+------------+
| > Mercury      |            |            | > 0.000    |            |
|                |            |            | > 018      |            |
+----------------+------------+------------+------------+------------+
| > Nichrome     | > 8.39     |            | > 0.000    |            |
|                |            |            | > 039      |            |
+----------------+------------+------------+------------+------------+
| > Nichrome V   | > 8.5      |            | > 0.000    |            |
|                |            |            | > 039      |            |
+----------------+------------+------------+------------+------------+
| > Platinum     |            | > 0.000    | > 0.000    |            |
|                |            | > 011      | > 027      |            |
+----------------+------------+------------+------------+------------+
| >              |            |            | > 0.000 45 |            |
|  Polycarbonate |            |            |            |            |
| > plastic      |            |            |            |            |
+----------------+------------+------------+------------+------------+
| >              |            |            | > 0.000 24 |            |
|  Polypropylene |            |            |            |            |
| > plastic      |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Polystyrene  |            |            | > 0.000 21 |            |
| > plastic      |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Steel,       | > 7.84,    |            | > 0.000    |            |
| > stainless    | > 7.95,    |            | > 045      |            |
| > (mass)       | > 8.0      |            |            |            |
+----------------+------------+------------+------------+------------+
| > Steel,       |            | > 0.000    | > 0.000    | > 0.000    |
| > stainless    |            | > 018      | > 047 7    | > 026 5    |
| > (provers)    |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Steel, tape, |            | > 0.000    | > 0.000    |            |
| > mild         |            | > 0116     | > 033 5    |            |
+----------------+------------+------------+------------+------------+
| > Steel,       |            |            |            | > 0.000    |
| > pressure     |            |            |            | > 016      |
| > vessel, low  |            |            |            |            |
| > carbon       |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Steel,       |            | > 0.000    | > 0.000    | > 0.000    |
| > prover, low  |            | > 012      | > 033 5    | > 018 6    |
| > carbon       |            |            |            |            |
+----------------+------------+------------+------------+------------+
| > Steel, terne |            | > 0.000    | > 0.000    | > 0.000    |
| > plate        |            | > 012      | > 035      | > 019 5    |
+----------------+------------+------------+------------+------------+
| > Tantalum     | > 16.6     |            | > 0.000    |            |
|                |            |            | > 020      |            |
+----------------+------------+------------+------------+------------+
| > Water (20    |            |            | > 0.000 21 |            |
| > °C)          |            |            |            |            |
+----------------+------------+------------+------------+------------+

Reference values for cubical coefficient of expansion given in per °F
are provided as reference for prover calibrations used for petroleum
products where the reference temperature is 60 °F.

**Table 9.11 A Short Table of Random Numbers**

46 96 85 77 27 92 86 26 45 21 89 91 71 42 64 64 58 22 75 81 74 91 48 46
18

44 19 15 32 63 55 87 77 33 29 45 00 31 34 84 05 72 90 44 27 78 22 07 62
17

34 39 80 62 24 33 81 67 28 11 34 79 26 35 34 23 09 94 00 80 55 31 63 27
91

74 97 80 30 65 07 71 30 01 84 47 45 89 70 74 13 04 90 51 27 61 34 63 87
44

22 14 61 60 86 38 33 71 13 33 72 08 16 13 50 56 48 51 29 48 30 93 45 66
29

40 03 96 40 03 47 24 60 09 21 21 18 00 05 86 52 85 40 73 73 57 68 36 33
91

52 33 76 44 56 15 47 75 78 73 78 19 87 06 98 47 48 02 62 03 42 05 32 55
02

37 59 20 40 93 17 82 24 19 90 80 87 32 74 59 84 24 49 79 17 23 75 83 42
00

11 02 55 47 48 84 74 36 22 67 19 20 15 92 53 37 13 75 54 89 56 73 23 39
07

10 33 79 26 34 54 71 33 89 74 68 48 23 17 49 18 81 05 52 85 70 05 73 11
17

67 59 28 25 47 89 11 65 65 20 42 23 96 41 64 20 30 89 87 64 37 93 36 96
35

93 50 75 20 09 18 54 34 68 02 54 87 23 05 43 36 98 29 97 93 87 08 30 92
98

24 43 23 72 80 64 34 27 23 46 15 36 10 63 21 59 69 76 02 62 31 62 47 60
34

39 91 63 18 38 27 10 78 88 84 42 32 00 97 92 00 04 94 50 05 75 82 70 80
35

74 62 19 67 54 18 28 92 33 69 98 96 74 35 72 11 68 25 08 95 31 79 11 79
54

91 03 35 60 81 16 61 97 25 14 78 21 22 05 25 47 26 37 80 39 19 06 41 02
00

42 57 66 76 72 91 03 63 48 46 44 01 33 53 62 28 80 59 55 05 02 16 13 17
54

06 36 63 06 15 03 72 38 01 58 25 37 66 48 56 19 56 41 29 28 76 49 74 39
50

92 70 96 70 89 80 87 14 25 49 25 94 62 78 26 15 41 39 48 75 64 69 61 06
38

91 08 88 53 52 13 04 82 23 00 26 36 47 44 04 08 84 80 07 44 76 51 52 41
59

68 85 97 74 47 53 90 05 90 84 87 48 25 01 11 05 45 11 43 15 60 40 31 84
59

59 54 13 09 13 80 42 29 63 03 24 64 12 43 28 10 01 65 62 07 79 83 05 59
61

39 18 32 69 33 46 58 19 34 03 59 28 97 31 02 65 47 47 70 39 74 17 30 22
65

67 43 31 09 12 60 19 57 63 78 11 80 10 97 15 70 04 89 81 78 54 84 87 83
42

61 75 37 19 56 90 75 39 03 56 49 92 72 95 27 52 87 47 12 52 54 62 43 23
13

78 10 91 11 00 63 19 63 74 58 69 03 51 38 60 36 53 56 77 06 69 03 89 91
24

93 23 71 58 09 78 08 03 07 71 79 32 25 19 61 04 40 33 12 06 78 91 97 88
95

37 55 48 82 63 89 92 59 14 72 19 17 22 51 90 20 03 64 96 60 48 01 95 44
84

62 13 11 71 17 23 29 25 13 85 33 35 07 69 25 68 57 92 57 11 84 44 01 33
66

29 89 97 47 03 13 20 86 22 45 59 98 64 53 89 64 94 81 55 87 73 81 58 46
42

16 94 85 82 89 07 17 30 29 89 89 80 98 36 25 36 53 02 49 14 34 03 52 09
20

04 93 10 59 75 12 98 84 60 93 68 16 87 60 11 50 46 56 58 45 88 72 50 46
11

95 71 43 68 97 18 85 17 13 08 00 50 77 50 46 92 45 26 97 21 48 22 23 08
32

86 05 39 14 35 48 68 18 36 57 09 62 40 28 87 08 74 79 91 08 27 12 43 32
03

59 30 60 10 41 31 00 69 63 77 01 89 94 60 19 02 70 88 72 33 38 88 20 60
86

05 45 35 40 54 03 98 96 76 27 77 84 80 08 64 60 44 34 54 24 85 20 85 77
32

71 85 17 74 66 27 85 19 55 56 51 36 48 92 32 44 40 47 10 38 22 52 42 29
96

80 20 32 80 98 00 40 92 57 51 52 83 14 55 31 99 73 23 40 07 64 54 44 99
21

13 50 78 02 73 39 66 82 01 28 67 51 75 66 33 97 47 58 42 44 88 09 28 58
06

67 92 65 41 45 36 77 96 46 21 14 39 56 36 70 15 74 43 62 69 82 30 77 28
77

72 56 73 44 26 04 62 81 15 35 79 26 99 57 28 22 25 94 80 62 95 48 98 23
86

28 86 85 64 94 11 58 78 45 36 34 45 91 38 51 10 68 36 87 81 16 77 30 19
36

69 57 40 80 44 94 60 82 94 93 98 01 48 50 57 69 60 77 69 60 74 22 05 77
17

71 20 03 30 79 25 74 17 78 34 54 45 04 77 42 59 75 78 64 99 37 03 18 03
36

89 98 55 98 22 45 12 49 82 71 57 33 28 69 50 59 15 09 25 79 39 42 84 18
70

58 74 82 81 14 02 01 05 77 94 65 57 70 39 42 48 56 84 31 59 18 70 41 74
60

50 54 73 81 91 07 81 26 25 45 49 61 22 88 41 20 00 15 59 93 51 60 65 65
63

49 33 72 90 10 20 65 28 44 63 95 86 75 78 69 24 41 65 86 10 34 10 32 00
93

11 85 01 43 65 02 85 69 56 88 34 29 64 35 48 15 70 11 77 83 01 34 82 91
04

34 22 46 41 84 74 27 02 57 77 47 93 72 02 95 63 75 74 69 69 61 34 31 92
13

From: NBS Handbook 91, p T‑82