Question

A statistics student wants to examine if there is a difference in the commute times for students and faculty at her community college. She collected data from a random sample of 10 faculty and 10 students. The commute times (in minutes) are given below.

Faculty 5 12 12 15 12 22 25 30 35 45
Students 10 12 14 15 15 20 22 24 25 30
Determine and enter the five-number summary for the commute times (in minutes) of the two samples. Include all calculations in your answer, round to two decimal places.

Answer 1

Explanation:

To find the five-number summary for the commute times (in minutes) of the two samples, we would determine the lowest, highest, first quartile, median and third quartile for each set of values.

1) Considering the data for faculty, arranging in ascending order, it becomes

5 12 12 12 15 22 25 30 35 45

Minimum = 5

Maximum = 45

Median = (15 + 22)/2 = 18.5

Placing the median in the data, it becomes

5 12 12 12 15 18.5 22 25 30 35 45

The median divides the data into the lower and upper halves

First quartile is the 25% mark. It is also the middle of the lower halve. Therefore,

First quartile = 12

Third quartile is the 75% mark. It is also the middle of the upper halve. Therefore,

Third quartile = 30

2) Considering the data for students, arranging in ascending order, it becomes

10 12 14 15 15 20 22 24 25 30

Minimum = 10

Maximum = 30

Median = (15 + 20)/2 = 17.5

Placing the median in the data, it becomes

10 12 14 15 15 17.5 20 22 24 25 30

The median divides the data into the lower and upper halves

First quartile is the 25% mark. It is also the middle of the lower halve. Therefore,

First quartile = 14

Third quartile is the 75% mark. It is also the middle of the upper halve. Therefore,

Third quartile = 24