Module 2 : Traffic Measurement Procedures

Lecture 06 : Measurement over a Short Section

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	Measure of Dispersion Measures describe the extent to which data spreads around the center of the distribution. Measures of dispersion include the different percentile speeds i.e. 15th, 85th,etc. and the standard deviation. Standard Deviation The most common statistical measure of dispersion in a distribution is the standard deviation. It is a measure of how far data spreads around the mean value. In simple terms, the standard deviation is the average value of the difference between individual observations and the average value of those observations. The Standard deviation, $\sigma_s$, of the sample can be calculated by $$\sigma_s = \sqrt{\frac{\Sigma f_i(v_i -v_v)^2}{n -1}}$$ (1) Percentile Speeds The 85th and 15th percentile speeds give a general description of the high and low speeds observed by most reasonable drivers. It is generally thought that the upper and lower 15% of the distribution represents speeds that are either too fast or too slow for existing conditions. These values are found graphically from the cumulative frequency distribution curve of Figure 6.4. The curve is entered on the vertical axis at values of 85% and 15%. The respective speeds are found on the horizontal axis. The 85th and 15th percentile speeds can be used to roughly estimate the standard deviation of the distribution $\sigma_{est}$, although this is not recommended when the data is available for a precise determination. $$\sigma_{est}=\frac{v_{85}-v_{15}}{2}$$ (2) The 85th and 15th percentile speeds give insight to both the central tendency and dispersion of the distribution. As these values get closer to the mean, less dispersion exists and the stronger the central tendency of the distribution becomes. The 98th percentile speed is also determining from the cumulative frequency curve, this speed is generally used for geometric design of the road.