What is SD of given set of numbers whose average is 5?

Standard deviation shows how much variation there is from the mean. 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.

We need to know a couple of important properties for this question:

If we add or subtract a constant to each term in a set:

• The mean will increase or decrease by the same constant.
• The standard deviation (SD) will not change.

If we increase or decrease each term in a set by the same percentage (multiply all terms by the same constant):

• The mean will increase or decrease by the same percentage.
• The SD will increase or decrease by the same percentage.

You can try it yourself:
The SD of a set: {1,1,4} will be the same as that of {5,5,8}, as the second set is obtained by adding 4 to each term of the first set.

This is because the standard deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term, we are shifting the mean of the set by this constant (the mean will increase or decrease by the same constant), but the variation from the mean remains the same, as all terms are also shifted by the same constant.

Also: If the range or SD of a list is 0, then the list will contain all identical elements. Conversely, if a list contains all identical elements, then the range and SD of the list is 0. If the list contains 1 element: The range is zero and the SD is zero.

This is because if a list contains all identical elements, then there is no variation from the mean, hence SD=0.

BACK TO THE ORIGINAL QUESTION:

What is SD of given set of numbers whose average is 5?


(1) None of the numbers are greater than this Average

If no number is more than the mean, then no number is less than the mean, which implies that this list contains all identical elements (or, equivalently, just one element), so SD=0. Sufficient.

(2) The Standard deviation is 0 when value of each of the given number is increased by 7 -->

If we add or subtract a constant to each term in a set, the SD will not change, so SD=0. Sufficient.

Answer: D.

For more on Standard Deviation check:

https://gmatclub.com/forum/math-standard-deviation-87905.html
https://gmatclub.com/forum/ps-questions ... 85897.html
https://gmatclub.com/forum/ds-questions ... 85896.html

Hope it helps.