Question

If the standard deviation of first n natural numbers is 2, then the value of n is

• A. 6
• B. 7
• C. 5
• D. 4

Answer 1

The Correct Option is B

standard deviation of first n natural number =\(\sqrt {\frac {n^2-1}{12}}\)
Given standard deviation of first n natural number = 2
2=\(\sqrt {\frac {n^2-1}{12}}\)
4=\(\frac {n^2-1}{12}\)
48=n²-1,
n²=49
n=7
Therefore, the correct option is (B) 7