Document: Standard deviation

Question: what does it mean to be one standard deviation below the mean
Answer: If the population of interest is approximately normally distributed, the standard deviation provides information on the proportion of observations above or below certain values. For example, the average height for adult men in the United States is about 70 inches ( 177.8 cm ), with a standard deviation of around 3 inches ( 7.62 cm ). This means that most men ( about 68 %, assuming a normal distribution ) have a height within 3 inches ( 7.62 cm ) of the mean ( 67 -- 73 inches ( 170.18 -- 185.42 cm ) ) -- one standard deviation -- and almost all men ( about 95 % ) have a height within 6 inches ( 15.24 cm ) of the mean ( 64 -- 76 inches ( 162.56 -- 193.04 cm ) ) -- two standard deviations. If the standard deviation were zero, then all men would be exactly 70 inches ( 177.8 cm ) tall. If the standard deviation were 20 inches ( 50.8 cm ), then men would have much more variable heights, with a typical range of about 50 -- 90 inches ( 127 -- 228.6 cm ). Three standard deviations account for 99.7 % of the sample population being studied, assuming the distribution is normal ( bell - shaped ). ( See the 68 - 95 - 99.7 rule, or the empirical rule, for more information. )

Question: what does the little u mean in statistics
Short answer: a random variable with
Answer: Let X be a random variable with mean value μ:

Question: the standard deviation of all possible values is called the
Answer: In addition to expressing the variability of a population, the standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. This derivation of a standard deviation is often called the `` standard error '' of the estimate or `` standard error of the mean '' when referring to a mean. It is computed as the standard deviation of all the means that would be computed from that population if an infinite number of samples were drawn and a mean for each sample were computed. It is very important to note that the standard deviation of a population and the standard error of a statistic derived from that population ( such as the mean ) are quite different but related ( related by the inverse of the square root of the number of observations ). The reported margin of error of a poll is computed from the standard error of the mean ( or alternatively from the product of the standard deviation of the population and the inverse of the square root of the sample size, which is the same thing ) and is typically about twice the standard deviation -- the half - width of a 95 percent confidence interval. In science, researchers commonly report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant -- normal random error or variation in the measurements is in this way distinguished from likely genuine effects or associations. The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.

Question: how do you find the sd in statistics
Short answer: square root of the difference between the average of the squares of the values and the square of the average value.
Answer: This means that the standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value. See computational formula for the variance for proof, and for an analogous result for the sample standard deviation.

Question: standard deviation is 1 what does it mean
Answer: The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. There are also other measures of deviation from the norm, including average absolute deviation, which provide different mathematical properties from standard deviation.

Question: how do you find the standard deviation of a mean
Answer: The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. There are also other measures of deviation from the norm, including average absolute deviation, which provide different mathematical properties from standard deviation.

Question: as a statistical unit of measure what does sigma represents
Answer: In statistics, the standard deviation ( SD, also represented by the Greek letter sigma σ or the Latin letter s ) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean ( also called the expected value ) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.