# Mean, Median & Mode - Descriptive Statistics

Here is an interesting question from Descriptive Statistics. The question tests your basic understanding of Mean, Median and Mode

Question
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?
A. \$4000
B. \$13000
C. \$9000
D. \$5000
E. \$11000

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