Certainly! Let's address each part of the question step by step:
### a. Determine the mean of the student scores, to the nearest tenth.
To find the mean (average) of the student scores, follow these steps:
1. Add up all the student scores.
[tex]\[
72 + 80 + 85 + 93 + 78 + 80 = 488
\][/tex]
2. Divide the total by the number of students, which is 6 in this case.
[tex]\[
\frac{488}{6} \approx 81.3
\][/tex]
So, the mean of the student scores is 81.3 (to the nearest tenth).
### b. Determine the median of the student scores.
To find the median, we need to arrange the scores in ascending order and find the middle value. For six students, the median will be the average of the 3rd and 4th scores:
1. Arrange the scores in ascending order:
[tex]\[
72, 78, 80, 80, 85, 93
\][/tex]
2. Since there is an even number of scores (6), the median is the average of the 3rd and 4th scores.
[tex]\[
\text{Median} = \frac{80 + 80}{2} = 80
\][/tex]
So, the median of the student scores is 80.0.
### c. Describe the effect on the mean and the median if Ms. Mosher adds 5 bonus points to each of the six students' scores.
When 5 bonus points are added to each score, the new scores are:
[tex]\[
77, 85, 90, 98, 83, 85
\][/tex]
#### New Mean:
1. Add up the new scores:
[tex]\[
77 + 85 + 90 + 98 + 83 + 85 = 518
\][/tex]
2. Divide the total by the number of students:
[tex]\[
\frac{518}{6} \approx 86.3
\][/tex]
The new mean is 86.3.
#### New Median:
1. Arrange the new scores in ascending order:
[tex]\[
77, 83, 85, 85, 90, 98
\][/tex]
2. Since there is an even number of scores, the median is the average of the 3rd and 4th scores.
[tex]\[
\text{Median} = \frac{85 + 85}{2} = 85
\][/tex]
The new median is 85.0.
### Summary
- Original Mean: 81.3
- Original Median: 80.0
- New Mean with Bonus Points: 86.3
- New Median with Bonus Points: 85.0
Adding 5 bonus points to each score has the effect of increasing both the mean and the median by exactly 5 points.
