Module 2 : Traffic Measurement Procedures

Lecture 06 : Measurement over a Short Section

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	Distribution Characteristics Common descriptive statistics may be computed from the data in the frequency distribution table or determined graphically from the frequency and cumulative frequency distribution curves. These statistics are used to describe two important characteristics of the distribution: Measure of Central Tendency Measure which helps to describe the approximate middle or center of the distribution. Measures of central tendency include the average or mean speed, the median speed, the modal speed, and the pace. Figure 1: Frequency and Cumulative Frequency Distribution curve Mean Speed The arithmetic (or harmonic) average speed is the most frequently used speed statistics. It is the measure of central tendency of the data. Mean calculated gives two kinds of mean speeds. $$v_t=\frac{\Sigma f_i v_i}{n}$$ (1) where, $v_t$ is the mean or average speed, $v_i$ is the individual speed of the $i_{th}$ vehicle, $f_i$ is the frequency of speed, and n is the total no of vehicle observed (sample size). Time mean Speed If data collected at a point over a period of time, e.g. by radar meter or stopwatch, produce speed distribution over time, so the mean of speed is time mean speed. Space mean Speed If data obtained over a stretch (section) of road almost instantaneously, aerial photography or enoscope, result in speed distribution in space and mean is space mean speed. Distribution over space and time are not same. Time mean speed is higher than the space mean speed. The spot speed sample at one end taken over a finite period of time will tend to include some fast vehicles which had not yet entered the section at the start of the survey, but will exclude some of the slower vehicles. The relationship between the two mean speeds is expressed by: $$v_t = v_s+\frac{\sigma_s^2}{v_s}$$ (2) where, $v_t$ and $v_s$ are the time mean speed and space mean speed respectively. And $\sigma_s$ is the standard deviation of distribution space. Median Speed The median speed is defined as the speed that divides the distribution in to equal parts (i.e., there are as many observations of speeds higher than the median as there are lower than the median). It is a positional value and is not affected by the absolute value of extreme observations. By definition, the median equally divides the distribution. Therefore, 50% of all observed speeds should be less than the median. In the cumulative frequency curve, the 50th percentile speed is the median of the speed distribution. Median Speed = v50 Pace The pace is a traffic engineering measure not commonly used for other statistical analyses. It is defined as the 10Km/h increment in speed in which the highest percentage of drivers is observed. It is also found graphically using the frequency distribution curve. As shown in fig 6.5. The pace is found as follows: A 10 Km/h template is scaled from the horizontal axis. Keeping this template horizontal, place an end on the lower left side of the curve and move slowly along the curve. When the right side of the template intersects the right side of the curve, the pace has been located. This procedure identifies the 10 Km/h increments that intersect the peak of the curve; this contains the most area and, therefore, the highest percentage of vehicles. Modal Speed The mode is defined as the single value of speed that is most likely to occur. As no discrete values were recorded, the modal speed is also determined graphically from the frequency distribution curve. A vertical line is dropped from the peak of the curve, with the result found on the horizontal axis.