Question

A highway speed monitor is located on the side of the road that has a speed limit of 45 mph. The system records the speeds of passing vehicles. The data below shows the speeds of the first 9 cars that pass. 46 56 45 44 45 61 55 53 39 What is the standard deviation, to the nearest tenth, based on the posted speed limit, 45 mph? a0 The tenth car traveling on this road breaks down and is being pushed by its owners as it passes the speed monitor. A speed of 1.5 mph is recorded. The measure of central tendency most affected by this tenth speed is the a1 What is the new standard deviation, to the nearest tenth, after the tenth speed is recorded? a2

Answer 1

a0 - 8.0

a1 - mean

a2 - 15.7

Answer 2

We first take the sum of the squares of the differences between the sample data and the limit 45 mph: 1^2 + 11^2 + 0^2 + (-1)^2 + 0^2 + 16^2 + 10^2 + 8^2 + (-6)^2 = 579. Dividing by 8 (# of cars less 1) gives 72.375, which is the variance. Taking the square root gives the SD of 8.5.
The measure of central tendency most affected by the 10th value of 1.5 mph is the mean. The median and mode are relatively unaffected since both involve the frequency of terms, and having a tenth term that is far below (like 1.5) will not affect it much as compared to if it was near the rest of the values (like anything below 39).
The new SD including the tenth car involves adding the deviation of (-43.5)^2 to the sum of 579, which gives 2471.25. Dividing by 9 (there are now 10 data points) and taking the square root gives the new SD of 16.6.