## 4 Results of Experimental Studies  
### Statistical Characteristics and Graphs of Distributions  
Standard methods of mathematical statistics were used to process experimental data on the distribution of FFS on sections of the road network of the city of Kharkiv. Statistical analysis of data samples involves calculating the characteristics of the distribution center, and its structure and evaluating the degree of variation and differentiation. Indicators of the main tendency of the distributions are the arithmetic mean, mode, and median. The main indicators of distribution variation are variance, standard deviation, and coefficient of variation. Indicators such as median, quartiles, deciles, and other percentiles are used to characterize the distribution structure. Studying the shape of the distribution involves assessing asymmetry and kurtosis. The listed indicators have an independent analytical value and allow obtaining a complex characteristic of the empirical distribution. The calculated statistical characteristics of free traffic speed distributions for the four studied sections of the road network of the city of Kharkiv are shown in Table 2.  
Since the mean values \(m\) as well as the standard deviation \(\sigma\) of the FFS values are now known for all four measuring sites, we can assess the representativeness of the resulting \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station Number** & **Stat. 1** & **Stat. 2** & **Stat. 3** & **Stat. 4** \\ \hline Station location & Ave. Heroiv Kharkova & \multicolumn{2}{c}{Ave.} & \multicolumn{1}{c}{St. 12-ho Kvitnia} & \multicolumn{1}{c}{St. Myru} \\  & & & & \\ \hline Valid N & 50 & 50 & 50 & 50 \\ Mean & 71.74 & 70.40 & 58.38 & 65.04 \\ Confidence 95.000\% & 68.94 & 67.28 & 55.55 & 62.34 \\ Geometric mean & 74.54 & 73.52 & 61.21 & 67.74 \\ Median & 71.10 & 69.57 & 57.56 & 64.36 \\ Mode & 70.00 & 70.50 & 57.50 & 65.50 \\ Minimum & 51 & 50 & 37 & 46 \\ Maximum & 96 & 97 & 86 & 85 \\
15 th percentile & 62.00 & 58.00 & 48.00 & 55.00 \\
50 th percentile & 70.00 & 70.50 & 57.50 & 65.50 \\
85 th percentile & 81.00 & 81.00 & 68.00 & 76.00 \\
95 th percentile & 91.00 & 90.00 & 76.00 & 80.00 \\ Range & 45.00 & 47.00 & 49.00 & 39.00 \\ Quartile range & 12.00 & 14.00 & 12.00 & 17.00 \\ Std. Dev. & 9.84 & 10.96 & 9.97 & 9.49 \\ Coef. Var. & 13.71 & 15.57 & 17.08 & 14.59 \\ Standard error & 1.39 & 1.55 & 1.41 & 1.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical characteristics of free-flowing speed distributions. samples. One method is to calculate the minimum sample size \(n_{\text{min}}\) for a given value of the maximum acceptable error \(\eta\) as follows:  
\[n_{\text{min}}=\frac{t_{a}^{2}\cdot\sigma^{2}}{\eta^{2}} \tag{1}\]  
where \(t_{a}\) is the confidence probability function, which for the standard in statistical studies value of the probability function \(\alpha=0.95\) will be \(t_{a}\)=1.96. The value \(\eta\) can be represented as the product of the mean \(m\) and the relative required accuracy \(\Delta\). If we take \(\Delta=5\%\), then, for the first sample (stat. 1), we obtain the following:  
\[n_{\text{min}}=\frac{1.96^{2}\cdot 9.84^{2}}{\left(0.1\cdot 71.74\right)^{2}}=29 \tag{2}\]  
We obtain similar values for samples at other measuring stations: \(n_{\text{min2}}=37\), \(n_{\text{min3}}=45\), and \(n_{\text{min3}}=33\). Since the actual number of observations \(n_{\text{min3}}=50\) exceeds \(n_{\text{min}}\), the sample size is sufficient to ensure the required reliability of the results. Table 2 shows the close location of the modal and median values, which is a sign of normal distribution and can also be an indirect confirmation of the representativeness of the samples. The \"Box-and-Whisker Plot\" is an effective tool for a compact image and analysis of a statistical population, which provides both diagnostic and descriptive information about the studied distributions (Figure 2). The lower and upper bounds of the boxes in Figure 2 correspond to the lower and upper quartiles of the distributions.