Question

eli is a loan officer. he determines his clients eligibility for loans and for good interest rates by using their credit scores. the scores of several clients are shown in the following table.

help eli evaluate his applicants based on their mean and median credit scores.
a. valerie has the highest mean score, but roy has the highest median score.
b. dirk has the highest mean score and the highest median score.
c. roy has the highest mean score, but valerie has the highest median score.
d. dirk has the highest mean score, but valerie has the highest median score.

Explanation:

Read and organize the data

Using the Table Reading knowledge point
The credit scores for each client across the three bureaus (Experian, Equifax, TransUnion) are:

• Roy: \(750, 792, 661\)
• Dirk: \(771, 707, 755\)
• Haley: \(643, 642, 770\)
• Valerie: \(646, 773, 762\)

Calculate the mean credit score for each client

We calculate the mean (average) score by summing the three scores and dividing by \(3\):

• Roy: \(\frac{750 + 792 + 661}{3} = \frac{2203}{3} \approx 734.33\)
• Dirk: \(\frac{771 + 707 + 755}{3} = \frac{2233}{3} \approx 744.33\)
• Haley: \(\frac{643 + 642 + 770}{3} = \frac{2055}{3} = 685.00\)
• Valerie: \(\frac{646 + 773 + 762}{3} = \frac{2181}{3} = 727.00\)

Comparing the means, Dirk has the highest mean score (\(744.33\)).

Determine the median credit score for each client

To find the median, we arrange each client's three scores in ascending order and select the middle value:

• Roy: \(661, 750, 792

ightarrow \text{Median} = 750\)

• Dirk: \(707, 755, 771

ightarrow \text{Median} = 755\)

• Haley: \(642, 643, 770

ightarrow \text{Median} = 643\)

• Valerie: \(646, 762, 773

ightarrow \text{Median} = 762\)

Comparing the medians, Valerie has the highest median score (\(762\)).

Compare results with the given options

We combine our findings:

• Dirk has the highest mean score (\(744.33\)).
• Valerie has the highest median score (\(762\)).

This matches option (d): "Dirk has the highest mean score, but Valerie has the highest median score."

Answer:

• a. Valerie has the highest mean score, but Roy has the highest median score.
• b. Dirk has the highest mean score and the highest median score.
• c. Roy has the highest mean score, but Valerie has the highest median score.
• d. Dirk has the highest mean score, but Valerie has the highest median score. (Correct answer)