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?  Answers:
A) $4000  B) $13,000  C) $9000  D) $5000  E) $11,000
The arithmetic mean of the incentives is $7000.   The median of the incentives is also $7000.   There is only one mode and the mode is $12,000.   Let their incentives be a, b, c, d, and e such that a ≤ b ≤ c ≤ d ≤ e   Therefore, the median of these values is 'c'.   So, c = $7000.   The sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000   There is only one mode amongst these 5 observations.   The mode is that value that appears with the maximum frequency.   Hence, $12,000 is the incentive received by the most number of salesmen.   The incentive that c has got is $7000   So, the incentive received by d and e has to be greater than or equal to $7000   But the mode is $12,000   So, d and e should have got $12,000 each.   Therefore, c + d + e = 7000 + 12,000 + 12,000 = $31,000   Hence, a + b = 35,000 - 31,000 = $4000   As there is only one mode, the incentives received by a and b have to be different   So, a received $1000 and b received $3000.   Maximum incentive : $12,000   Minimum incentive : $1000   Difference between maximum and minimum incentive : $11,000   Answer $11,000
<result>E</result>
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?