An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives...
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?
Answer/Solution
$11,000
Steps/Work
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 E
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 E