Let’s go through the questions step by step, based on the survey results provided for the number of hours spent at work last week by college graduates and non-graduates.
### (a) What were the ranges for the two groups?
The range of a data set is the difference between the maximum and minimum values in the set.
Graduates:
To find the range for graduates, we look at their data:
[tex]\[42, 41, 42, 48, 59, 56, 55, 53, 50, 68, 63, 62, 61, 61, 60, 60, 79, 77, 76, 70\][/tex]
The maximum value for graduates is 79 hours, and the minimum value is 41 hours.
[tex]\[ \text{Range for Graduates} = 79 - 41 = 38 \][/tex]
Non-graduates:
For non-graduates, the data is:
[tex]\[23, 22, 21, 33, 32, 34, 36, 37, 38, 39, 44, 41, 41, 44, 46, 48, 48, 49, 50, 59\][/tex]
The maximum value for non-graduates is 59 hours, and the minimum value is 21 hours.
[tex]\[ \text{Range for Non-graduates} = 59 - 21 = 38 \][/tex]
Answer:
- Graduates: 38
- Non-graduates: 38
### (b) Which group had the higher median number of hours?
The median is the middle value of a data set when it is ordered from least to greatest. If the number of data points is even, the median is the average of the two middle numbers.
Graduates:
The sorted list of hours for graduates is:
[tex]\[41, 41, 42, 42, 48, 50, 53, 55, 56, 59, 60, 60, 61, 61, 62, 63, 68, 70, 76, 77, 79\][/tex]
Since there are 21 values:
[tex]\(\frac{21 + 1}{2} = 11\)[/tex]
The median is the 11th element, which is 60.
Non-graduates:
The sorted list of hours for non-graduates is:
[tex]\[21, 22, 23, 32, 33, 34, 36, 37, 38, 39, 41, 41, 44, 44, 46, 48, 48, 49, 50, 59\][/tex]
Since there are 20 values:
[tex]\(\frac{20}{2} = 10\)[/tex] and [tex]\(\frac{20}{2} + 1 = 11\)[/tex]
The median is the average of the 10th and 11th elements:
[tex]\[ \frac{39 + 41}{2} = 40 \][/tex]
Answer:
- Graduates: 60
- Non-graduates: 40
- The group with the higher median is Graduates.
### (c) Which group had more responses in the 50s?
To determine this, we count the number of responses that fall within the 50-59 range for each group.
Graduates:
The number of responses in the 50s (50-59 inclusive) for graduates are:
[tex]\[50, 53, 55, 56, 59\][/tex]
There are 5 responses.
Non-graduates:
The number of responses in the 50s (50-59 inclusive) for non-graduates are:
[tex]\[50, 59\][/tex]
There are 2 responses.
Answer:
- Graduates: 5
- Non-graduates: 2
- The group with more responses in the 50s is Graduates.
### Summary of answers:
(a) What were the ranges for the two groups?
- Graduates: 38
- Non-graduates: 38
(b) Which group had the higher median number of hours?
- The group with the higher median is Graduates.
(c) Which group had more responses in the 50s?
- The group with more responses in the 50s is Graduates.
