Arrange the following from largest to smallest SD a) 50, 60, 70, 75, 8

Question

Arrange the following from largest to smallest SD

a = {50, 60, 70, 75, 80, 90, 100} 
b = {50, 60, 60, 75, 90, 90, 100} 
c = {50, 50, 60, 75, 90, 100, 100}

A. c > a > b 
B. a > b > c 
C. b > c > a 
D. a > c > b 
E. None of the above

chetan2u · Answer

How can there be two sources for the same question. Please tag the source correctly. 
Also the OA as A is wrong.

All three have same mean, which is 75. We have to see the spread around 75 for all of them. Greater the spread, higher the SD.

1) Between a and b, the two number closer to mean in ‘a’, viz 70 and 80, have been substituted by two other elements, 60 and 90, in b, and other remaining numbers are same. 
Thus SD of b>SD of a
a) 50, 60, 70, 75, 80,90, 100
b) 50, 60, 60, 75, 90, 90, 100

2) Between c and b, the two number closer to mean in ‘b’, viz 60 and 90, have been substituted by two other elements 50 and 100 in ‘c’, and other remaining numbers are same. 
Thus SD of c>SD of b
b) 50, 60, 60, 75, 90, 90, 100
c) 50, 50, 60, 75, 90, 100, 100

c>b>a

This option is not there in choices A to D, and thus answer is E.

siddhantvarma · Answer

KarishmaB   Bunuel  In this question, what's the trick where you can just look at the set and figure out their relative standard deviation? Calculating the mean can be lengthy. What's the optimal technique you'd recommend to use in such types of questions where the data sets are very similar?

Bunuel · Answer

Arrange the following from largest to smallest SD a = {50, 60, 70, 75, 80, 90, 100} b = {50, 60, 60, 75, 90, 90, 100} c = {50, 50, 60, 75, 90, 100, 100} A. c > a > b B. a > b > c C. b > c > a D. a > c > b E. None of the above The standard deviation of a list shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas a high standard deviation indicates that the data are spread out over a large range of values. All three lists given are symmetric around their mean of 75: a = {50, 60, 70, 75 , 80, 90, 100} b = {50, 60, 60 , 75 , 90 , 90, 100} c = {50, 50 , 60, 75 , 90, 100 , 100} However, the values 60 and 90 in list b are further from the mean of 75 than 70 and 80 in list a. Therefore, the standard deviation of a is less than that of b. Similarly, the values 50 and 100 in list c are further from the mean of 75 than 60 and 90 in list b. Therefore, the standard deviation of b is less than that of c. Hence, we have a < b < c. Asnwer: E.

KarishmaB · Answer

Since Bunuel has already shared the solution, I won't repeat it. Further, you can check out this video for a discussion on SD: https://youtu.be/0E6FQMzQVj0

Arrange the following from largest to smallest SD a) 50, 60, 70, 75, 8

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Arrange the following from largest to smallest SD a) 50, 60, 70, 75, 8

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards