Tony 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.
| Name | Experian | Equifax | TransUnion |
| :---- | :------- | :------ | :----------- |
| Neil | 726 | 752 | 822 |
| Paula | 634 | 732 | 771 |
| Jeff | 721 | 760 | 754 |
| Peter | 666 | 716 | 707 |
Help Tony evaluate his applicants based on their mean and median credit scores.
a. Jeff has the highest mean score, but Paula has the highest median score.
b. Neil has the highest mean score, but Jeff has the highest median score.
c. Neil has the highest mean score and the highest median score.
d. Paula has the highest mean score, but Jeff has the highest median score.
Answer (2)
Calculate the mean credit score for each client.
Calculate the median credit score for each client.
Identify the client with the highest mean credit score: Neil.
Identify the client with the highest median credit score: Jeff.
The answer is: N e i l ha s t h e hi g h es t m e an score , b u t J e ff ha s t h e hi g h es t m e d ian score .
Explanation
Understanding the Problem We are given a table of credit scores for four clients from three different agencies. Our goal is to determine which client has the highest mean credit score and which client has the highest median credit score.
Calculating the Mean First, we need to calculate the mean credit score for each client. The mean is calculated by summing the three scores for each client and dividing by 3.
Determining the Highest Mean The mean credit scores are:
Neil: ( 726 + 752 + 822 ) /3 = 766.67 Paula: ( 634 + 732 + 771 ) /3 = 712.33 Jeff: ( 721 + 760 + 754 ) /3 = 745.00 Peter: ( 666 + 716 + 707 ) /3 = 696.33
From these calculations, we can see that Neil has the highest mean credit score.
Calculating the Median Next, we need to calculate the median credit score for each client. The median is the middle value when the scores are sorted in ascending order.
Determining the Highest Median The median credit scores are:
Neil: median ( 726 , 752 , 822 ) = 752 Paula: median ( 634 , 732 , 771 ) = 732 Jeff: median ( 721 , 760 , 754 ) = 754 Peter: median ( 666 , 716 , 707 ) = 707
From these calculations, we can see that Jeff has the highest median credit score.
Conclusion Therefore, Neil has the highest mean score, and Jeff has the highest median score. This corresponds to option b.
Examples
Understanding mean and median credit scores is crucial in finance. For instance, when evaluating loan applications, banks use these measures to assess risk. A high mean score suggests consistent creditworthiness, while the median indicates the typical credit behavior. If you're managing a portfolio, knowing these statistics helps in making informed decisions about who to lend to, ensuring a balanced and reliable investment strategy.
Neil has the highest mean credit score at 766.67, while Jeff has the highest median credit score at 754. Therefore, the answer is b. Neil has the highest mean score, but Jeff has the highest median score.
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