Question

as part of a survey, 18 college graduates and 19 non - graduates were asked, \how many hours did you spend at your job last week?\ the results are shown in the stem - and - leaf display below. answer the questions that follow.
(a) what were the ranges for the two groups?
graduates non - graduates
(b) which group had the higher median number of hours?
graduates non - graduates the medians were the same
(c) which group had more responses in the 30s?
graduates non - graduates each had the same

Explanation:

Step1: Find range for graduates

For graduates, the smallest value is 21 (from the key, 2|1 means 21) and the largest value is 55. Range for graduates = 55 - 21 = 34.

Step2: Find range for non - graduates

For non - graduates, the smallest value is 15 (2|15 means 15) and the largest value is 59. Range for non - graduates = 59 - 15 = 44.

For part (b):

Step1: Arrange graduate data in ascending order

Graduate data: 21, 24, 24, 25, 31, 34, 34, 38, 40, 41, 41, 44, 44, 45, 55. There are 15 data points. Median is the 8th value, which is 40.

Step2: Arrange non - graduate data in ascending order

Non - graduate data: 15, 20, 20, 22, 23, 25, 26, 28, 29, 30, 30, 34, 35, 37, 40, 43, 44, 59. There are 18 data points. Median is the average of the 9th and 10th values. (29 + 30)/2 = 29.5. So graduates have a higher median.

For part (c):

Step1: Count responses in 30s for graduates

For graduates, the values in the 30s are 31, 34, 34, 38. There are 4 values.

Step2: Count responses in 30s for non - graduates

For non - graduates, the values in the 30s are 30, 30, 34, 35, 37. There are 5 values. Non - graduates have more responses in the 30s.

Answer:

(a) Graduates range: 34, Non - graduates range: 44
(b) Graduates
(c) Non - graduates