Which of the following sets has the greatest standard deviation?

The standard deviation is a sophisticated measure that relies in part on the distance of each data value from the mean. In general, the farther the data values are from the mean, the larger the standard deviation. So, let’s find the mean of each data set first.

A. (1 + 4 + 12 + 16 + 17)/5 = 50/5 = 10
B. (3 + 4 + 7 +18 +18)/5 = 50/5 = 10
C. (2 + 5 + 13 + 17 + 23)/5 = 50/5 =10
D. (-50 + 2 + 33 + 34 + 35)/5 = 50/5 = 10
E. (0 + 0 + 0 + 19+ 31)/5 = 50/5 = 10

As we can see, all the data sets have a mean of 10. Now, for each data set, we need to find how far away each value is from the mean. Let’s look at the data sets again.

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

As we can see, the data values from set D are the farthest from its mean out of all the data sets (four of its 5 values, -50, 33, 34, and 35, are farther from 10 than any values in the other data sets); thus, set D has the greatest standard deviation.

Answer: D

Jeff, for options C and D, I am getting a total of 60 and 54, resulting in a mean of 12 and 10.8 respectively.
But even then, option D has the highest deviation. Am I doing something wrong?

Is it necessary to calculate mean?
At a glance it was obvious that Set D had the most scattered vaues

The set with the greatest range should have the highest standard deviation.