A group of students collected data on the speed of vehicles traveling through a

Question

A group of students collected data on the speed of vehicles traveling through a construction zone on a state highway where the posted construction speed limit was 25 mph. The recorded speeds for 15 randomly selected vehicles (sorted) are given below:

20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 40, 41

1)Using a z-score, explain why a speed of 20 mph is unusual.

2) Compute the upper and lower outlier bounds.

3)The speed of 20 mph may or may not be an outlier based on the z-score and the outlier bounds. For this data set, explain why we might prefer the outlier bounds over z-scores, or vice versa.

Explanation / Answer

1)

mean = 32.6

sd = 6.2541

z-score for 20 = (20 - 32.6)/ 6.2541 =-2.01467

As a general rule, z-scores lower than -1.96 or higher than 1.96 are considered unusual

here z < -1.96 , hence unusual

2)

Q1 = 28 , Q2 = 33, Q3 = 38

IQR = Q3 -Q1 = 38-28 = 10

lower outlier bound = Q1 - 1.5* IQR = 28 - 1.5 *10 = 13

upper outlier bound = Q3 +1.5* IQR = 38 + 10 * 1.5 = 38 +15 = 53

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