The question is a Problem Solving question on Mean, Median and Mode - Descriptive Statistics.
Question 10
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?
- $4000
- $13,000
- $9000
- $5000
- $11,000
The correct choice is (E) and the correct answer is
$11,000.
Explanatory Answer
The arithmetic mean of the incentives of the 5 salesmen is $7000.
Therefore, the sum of the incentives received by all 5 taken together is 5 * 7000 = $35,000.
The median for these 5 observations is $7000.
Let us say their incentives in ascending order are a, b, c, d and e.
So, c = $7000
and a + b + c + d + e = $35,000
The only mode among the 5 observations is $12,000.
So, the maximum number of observations among the 5 will be in $12,000.
We have deduced that c has got $7000.
Hence, the only possibility is that both d and e got an incentive of $12,000 each.
So, incentives received by c + d + e = 7000 + 12000 + 12000 = $31,000
Therefore, a + b = 35,000 - 31,000 = 4000.
a and b have to be two different values as the only mode is $12,000.
So, a has to be $1000 and b has to be $3000.
The difference between the highest and the lowest incentives is, therefore 12,000 - 1000 = $11,000
Topicwise List of Questions
This ebook with about 110 questions in over 200 pages covers all major concepts in Descriptive Statistics (Mean, Median, Range, and Deviation). Includes typical GMAT type questions in both Problem Solving and Data Sufficiency formats.
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