To solve this problem, we need to determine both the mean and median credit scores for each client: Neil, Paula, Jeff, and Peter. Let's go step by step:
### Step 1: Calculate the Mean Scores
The mean score is calculated as the average of the scores from Experian, Equifax, and TransUnion for each person.
For Neil:
[tex]\[ \text{Mean} = \frac{726 + 752 + 822}{3} = \frac{2300}{3} = 766.67 \][/tex]
For Paula:
[tex]\[ \text{Mean} = \frac{634 + 732 + 771}{3} = \frac{2137}{3} \approx 712.33 \][/tex]
For Jeff:
[tex]\[ \text{Mean} = \frac{721 + 760 + 754}{3} = \frac{2235}{3} = 745.00 \][/tex]
For Peter:
[tex]\[ \text{Mean} = \frac{666 + 716 + 707}{3} = \frac{2089}{3} \approx 696.33 \][/tex]
### Step 2: Calculate the Median Scores
The median score is the middle value when the scores are arranged in ascending order for each person.
For Neil (scores: 726, 752, 822):
The median is 752.
For Paula (scores: 634, 732, 771):
The median is 732.
For Jeff (scores: 721, 754, 760):
The median is 754.
For Peter (scores: 666, 707, 716):
The median is 707.
### Step 3: Identify the Highest Mean and Median Scores
- Comparing the mean scores:
- Neil: 766.67
- Paula: 712.33
- Jeff: 745.00
- Peter: 696.33
Neil has the highest mean score with 766.67.
- Comparing the median scores:
- Neil: 752
- Paula: 732
- Jeff: 754
- Peter: 707
Jeff has the highest median score with 754.
### Step 4: Determine the Correct Option
Based on the findings:
- Neil has the highest mean score (766.67).
- Jeff has the highest median score (754).
Thus, the correct option is:
b. Neil has the highest mean score, but Jeff has the highest median score.
