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. A GMAT hard math question.
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?
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
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
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
GMAT® is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.
GRE® is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.
SAT® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.
Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Chennai 600 034. India