Question

Calvin is a train company manager.. He compares the arrival times of a morning train service for 10 days in the summer and 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? Show why you think this giving reasons with your answers.

Answer 1

Calvin's observations are correct; the median number of minutes late increases from 12.7 in the summer to 15.5 in the winter, and the winter service is less consistent with a range of 62 minutes versus summer's 11 minutes.

Step-by-step explanation:

To determine if Calvin's observations about the train's punctuality in winter are correct, we need to calculate the median and consistency (range of the number of minutes late) based on the given data points for the number of minutes late in the winter: 8, 32, 44, 5, 17, 67, 9, 14, 10, 26.

Firstly, we arrange the data in ascending order to find the median: 5, 8, 9, 10, 14, 17, 26, 32, 44, 67. With 10 data points, the median is the average of the 5th and 6th values, which are 14 and 17. Thus, the median number of minutes late in winter is (14 + 17) / 2 = 15.5 minutes.

Next, to judge the consistency, we calculate the range. The range is the difference between the maximum and minimum values, so in this case, it is 67 - 5 = 62 minutes. Compared to the summer range of 11 minutes, the winter range is significantly higher.

Calvin is right: the median number of minutes late increases from summer to winter (12.7 to 15.5 respectively), and the train service is less consistent in winter, indicated by a larger range (62 minutes) in comparison to summer (11 minutes).