Project 1b: Descriptive Statistics

(return to home page)

Description of the situation:

This report is based on problem 74 on page 120 of the textbook. The U.S. National Highway Traffic Safety Association provides a collection of data (P3_74.xls contained on the disk provided with the textbook) showing the number of speeding-related fatalities in each of the 51 states, categorized by road type and speed limit.

Objective:

Are U.S. traffic fatalities related to the speed limit and/or road type?

Description of variables:

There are two road types: Interstate and Non-interstate.

There are two Interstate speed categories: over 55 and at 55

There are six Non-Interstate speed categories: at 55, at 50, at 45, at 40, at 35, under 35

The following is calculated from the raw data provided. (I translates to Interstate and NI translates to Non-Interstate.)

1. Do the average number and/or variability in the number of traffic fatalities occurring on interstate highways tend to increase as the speed limit is raised above 55 miles per hour?

On interstate highways, the average number of traffic fatalities (mean) increases as the speed limit is raised above 55 miles per hour. That is, the mean rises from 13.412 to 16.765.

The variance decreases: at 55 miles per hour, the variance is 606.727 and over 55 miles per hour, the variance is 495.824.

2. Do the average number and/or variability in the number of traffic fatalities occurring on non-interstate roads tend to increase as the speed limit rises above 35 miles per hour?

On non-interstate roads, the average number of traffic fatalities tends to increase as the speed limit rises from under 35 miles per hour to 55 miles per hour as shown by the linear trend line (in bright red) below.

The variance also tends to increase as the speed rises from under 35 miles per hour to 55 miles per hour as shown by the linear trend line (in bright red) below. The greatest variability occurs in the non-interstate roads at 55 miles per hour category, and the lowest variability occurs in non-interstate roads at 50 miles per hour category. The chance of a fatality on a non-interstate road at 55 miles per hour varies greatly; however, the chance that a fatality on a non-interstate road at 50 miles per hour is more likely to be predicted by the mean in that category. So, although the chances are less predictable around the mean in non-interstate road at 55 miles per hour category, who wants to take that chance?

3. Do the average number and/or variability in the number of traffic fatalities occurring on a road with a posted speed limit of 55 miles per hour tend to change with the road type (i.e. interstate versus non-interstate)?

If the supposition is made that the numbers of fatalities recorded in this dataset are recorded at the speed at which the fatality occurred, the answer to this question can not be obtained from this dataset.

However, without that supposition in mind:

The average number of traffic fatalities on non-interstate roads at 55 miles per hour is much greater that the average of traffic fatalities on interstate roads at 55 miles per hour. The variance is also much greater on non-interstate roads at 55 miles per hour than on interstate roads at 55 miles per hour. Based on the higher variability, it is more difficult to predict that the number of fatalities on non-interstate roads at 55 miles per hour will center around the mean.

4. Based on the data, which combination of speed limit and road type appears to be most lethal for U.S. drivers?

Because the average number of fatalities is greatest on non-interstate roads at 55 miles per hour, it appears that that combination of road type and speed is the most lethal for U.S. drivers.

5. Based on the data, which combination of speed limit and road type appears to be safest for U.S. drivers?

Based on the same graph as above, because the average number of fatalities is lowest on non-interstate roads at 50 miles per hour, it appears that that combination of road type and speed is the safest for U.S. drivers.

The answers to letters d. and e. above may be correct based on what appears in the graph of average fatalities, but averages can be skewed by outliers. Below is a scatter plot of the points that each of 51 states reported fatalities in the non-interstate roads at 55 miles per hour category.

What if the two obvious outliers (at the top above) are thrown out of the calculation for the average? The new average drops from 110 to around 88, but the average fatalities occurring in the non-interstate road at 55 miles per hour category is still the greatest (see below).

END OF REPORT