Example 4.2 Determining Speed Characteristics from a Set of Speed Data Table 4.2 shows the data collected on a rural highway in Virginia during a speed study. Develop the frequency histogram and the frequency distribution of the data and determine: 1. The arithmetic mean speed 2. The standard deviation 3. The median speed 4. The pace 5. The mode or modal speed 6. The 85th-percentile speed Table 4,2 Speed Data Obtained on a Rural Highway Speed (mi/h) Speed (mi/h) Speed (mi/h) Speed (mi/h) Car No. Car No. Car No. Car No. 47.8 67 56.0 45 46 1 35.1 23 46.1 44.0 24 54.2 47.1 68 49.1 34.8 52.4 49.2 56.4 69 47 48 52.3 3. 4. 25 26 45.8 44.3 57.3 70 46.8 49 49.1 71 48.5 5. 6. 36.3 27 54.0 28 57.8 50 37.1 72 45.4 7. 42.1 29 36.8 51 65.0 73 48.6 52.0 49.8 74 52 53 49.5 52.2 48.4 30 55.8 50.1 51.8 9. 31 43.3 75 10 50.8 32 55.3 54 76 63.4 11 38.3 33 39.0 55 42.8 77 60.1 34 53.7 56 49.5 78 48.8 12 44.6 52.1 48.7 61.8 57 48.6 79 35 36 40.8 54.5 13 45.2 58 41.2 80 14 41.1 15 55.1 37 51.6 59 48.0 81 82 83 56.6 48.2 60 58.0 51.7 50.3 16 50.2 38 17 54.3 39 61 49.0 84 85 62.1 53.3 53.4 62 41.8 59.8 40.3 55.1 45.0 48.3 18 19 45.4 55.2 40 41 63 48.3 45.9 86 64 65 20 45.7 42 44.7 21 54.1 43 66 49.5 22 54.0 44
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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