Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below.
Private Transport
Public Transport
27
30
33
29
28
25
32
20
20
27
34
32
30
37
28
38
18
21
29
35
a. Considering the travel times (in minutes) of employees using private transport, compute the z-score for the tenth employee with travel time of 29 minutes.
b. Considering the travel times (in minutes) of employees using public transport, compute the z-score for the second employee with travel time of 29 minutes. How does this z-score compare with the z-score you calculated for part a?c. Based on z-scores, do the data for employees using private transport and public transport contain any outliers?
What will be an ideal response?
Mean = 27.9, StDev = 5.24
The z-score is then obtained as, 
b. For second employee using public transport: First, calculate the mean (AVERAGE function in Excel) and standard deviation (STDEV.S function in Excel) for public transport.
Mean = 29.4, StDev = 6.28
The z-score is then obtained as, 
Even though the employees had the same travel time, the z-score for the tenth employee in the sample who used a private transport is much larger because that employee is part of a sample with a smaller mean and a smaller standard deviation.
c.
Travel Times using Private Transport | z-score | Travel Times using Public Transport | z-score |
27 | -0.17 | 30 | 0.10 |
33 | 0.97 | 29 | -0.06 |
28 | 0.02 | 25 | -0.70 |
32 | 0.78 | 20 | -1.50 |
20 | -1.51 | 27 | -0.38 |
34 | 1.16 | 32 | 0.41 |
30 | 0.40 | 37 | 1.21 |
28 | 0.02 | 38 | 1.37 |
18 | -1.89 | 21 | -1.34 |
29 | 0.21 | 35 | 0.89 |
No z-score is less than -3.0 or above +3.0; therefore, the z-scores do not indicate the existence of any outliers in either sample.
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