Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are given the number of packages shipped by 5 companies. Let’s list those below:
Company A: 45 ,55, 50, 50
Company B: 10, 30, 30, 10
Company C: 34, 28, 28, 30
Company D: 39, 42, 41, 38
Company E: 50, 60, 60, 70
We may recall the the standard deviation represents how far the data points are from the mean. It’s not necessary to calculate the standard deviations of any of the data sets. Let’s “eyeball” the list instead. We see that the data points of Companies B and E are most spread apart. Thus, the largest standard deviation will come from either Company B or Company E.
Let’s calculate the mean (arithmetic average) for Company B and E.
Mean of Company B = (10 + 30 + 30 + 10)/4 = 80/4 = 20
For Company B, we see that the distances of the data points are 10, 10, 10, and 10, respectively, from the mean. (Note that we don’t care about the + or – signs of those distances.)
Mean of Company E = (50 + 60 + 60 + 70)/4 = 240/4 = 60
We see that the distances of the data points are 10, 0, 0, and 10, respectively, from the mean.
Thus, company B has a greater standard deviation than company E and hence the greatest standard deviation of the 5 companies.
Answer: B
