Question

part of a survey, 19 college graduates and 18 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. number of hours at work graduates non - graduates 9 4 | 2 | 2 5 5 9 8 6 5 3 2 0 | 3 | 0 0 2 3 7 8 9 9 5 4 2 1 1 1 0 | 4 | 1 1 5 7 8 6 2 | 5 | 0 0 9 key: 24 - 4 | 2 | 2 → 22 (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 50s? graduates non - graduates each had the same

Explanation:

Step1: Find graduates' range

For graduates, the smallest value is 24 and the largest is 58. Range = Largest - Smallest = 58 - 24 = 34.

Step2: Find non - graduates' range

For non - graduates, the smallest value is 22 and the largest is 59. Range = Largest - Smallest = 59 - 22 = 37.

Step3: Find graduates' median

There are 19 graduates. The median is the 10th value when ordered. Arranging the values, the 10th value is 35.

Step4: Find non - graduates' median

There are 18 non - graduates. The median is the average of the 9th and 10th values when ordered. Arranging the values, the 9th value is 37 and the 10th value is 38. Median=$\frac{37 + 38}{2}=37.5$. So non - graduates have a higher median.

Step5: Count responses in 50s

For graduates, there are 3 values in the 50s (52, 56, 58). For non - graduates, there are 3 values in the 50s (50, 50, 59). Each had the same number of responses in the 50s.

Answer:

(a) Graduates: 34, Non - graduates: 37
(b) Non - graduates
(c) Each had the same