Question

Calvin is a train company manager.

He compares the arrival times of a morning train service for 10 days in the summerand for 10 days in the winter.

In the summer the median number of minutes late was 12.7 minutes.The range of the number of minutes late was 11 minutes.

The results below show the number of minutes late in the winter.

8, 32, 44, 5, 17, 67, 9, 14, 10, 26,

Calvin thinks that in the winter
- the median number of minutes late increases
- the train service is less consistent.

Is Calvin correct?

Answer 1

From the results shown, we can conclude that Calvin is correct.

Why is Calvin correct?

To determine why Calvin is correct, we can begin by calculating the median value for minutes late in winter. This gives us the following;

5, 8, 9, 10, 14, 17, 26, 32, 44, 67

14 + 17/2

= 15.53

We compare this to the value in summer and realize that the median number of minutes late increases.

Also, the train service is less consistent because the range of data in summer is 11 minutes while in winter, it is up to 67 minutes.