An analysis of the monthly incentives received by 5 salesmen: The mean and median of the incentives is $7, The only mode among the observations is $12, 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?
Solution
Correct Answer: Option D
The arithmetic mean of 5 observations is $7000. Therefore, the sum of these 5 observations is 5 * 7000 = $35,000. The median 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 is $12,000. So, the maximum number of observations among the 5 will be in $12,000. The only possibility is that both d and e got an incentive of $12,000 each. So, 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 is therefore 12,000 - 1000 = $11,000
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