# GMAT Quant | GMAT Statistics Question

###### GMAT Sample Questions | Mean, Median, Mode & Range

This GMAT practice question is a very interesting problem solving question from descriptive statistics. It covers the following statistical concepts: Mean, Median, Mode, and Range.

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 ?

1. \$4000
2. \$13,000
3. \$9000
4. \$5000
5. \$11,000

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### Explanatory Answer | Mean Median Mode & Range

##### Hints to solve this GMAT Statistics question
1. Mean and Median = \$7000. So, find the third highest incentive.

2. Only one mode; mode = \$12,000

3. Use hint 1 and hint 2 to find how many have got \$12,000

4. Now compute the sum of incentives got by those who got neither \$7000 nor \$12000

##### Step 1 of solving this GMAT Statistics Question: Understanding the given data
1. The arithmetic mean of the incentives is \$7000.

2. The median of the incentives is also \$7000.

3. There is only one mode and the mode is \$12,000.

##### Step 2 of solving this GMAT Statistics Question: Decoding Mean and Median

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'.
The median incentive is \$7000. So, c = \$7000.

Essentially, the incentives are __   __   7000   __   __

The arithmetic mean of the incentives is \$7000.
So, the sum of their incentives a + b + c + d + e = 5 * 7000 = \$35,000

##### Step 3 of solving this GMAT Statistics Question: Decoding Mode

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.

So, the incentives are __   __   7000, 12000, 12000

##### Step 3 of solving this GMAT Statistics Question: Putting it all together

The incentive that c has got is \$7000
The incentive received by d and e are 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.

Maximum incentive : \$12,000
Minimum incentive : \$1000
Difference between maximum and minimum incentive : \$11,000

##### Choice E is the correct answer.

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