udaymathapati wrote:

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

1. None of the numbers are greater than this Average

2. The Standard deviation is 5 when value of each of the given number is increased by 7

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 high standard deviation indicates that the data are spread out over a large range of values.

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

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

Mean will increase or decrease by the same constant.

SD will not change.

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

Mean will increase or decrease by the same percent.

SD will increase or decrease by the same percent.You can try it yourself:

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

That's because 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 (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 Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.That's 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 mean, which implies that this list contains all identical elements (or which is the same 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 SD will not change, so SD=0. Sufficient.

Answer: D.

For more on Standard Deviation check:

math-standard-deviation-87905.htmlps-questions-about-standard-deviation-85897.htmlds-questions-about-standard-deviation-85896.htmlHope it helps.