# GMAT® Prep : Mean, Median, Mode & Range

Concept: Understating impact of mean and median being same. Finding 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: 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 #### Explanatory Answer Video explanation will be added soon #### Use these hints and try 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: Data given

1. The arithmetic mean of the incentives is $7000. 2. The median of the incentives is also$7000.

So, the sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000 #### Step 3: 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 4: 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 So, a received$1000 and b received $3000. Maximum incentive :$12,000

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

#### Complete Explanation

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. 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

### Are you targeting Q-51 in GMAT Quant? Make it a reality!

Comprehensive Online classes for GMAT Math. 20 topics.
Focused preparation for the hard-to-crack eggs in the GMAT basket!