What is the least value of the standard deviation of 5 integers, no two of which are equal ?

Options

A. `sqrt5`
B. 2
C. `sqrt2`
D. No such least value can be computed

Answer

C

Explanation

Let us consider any five integers which are 3, 4, 5, 6, 7.
`therefore" mean"=(3+4+5+6+7)/(5)=(25)/(5)=5`
`thereforeSD=sqrt(((5-3)^(2)+(5-4)^(2)+(5-5)^(2)+(5-6)^(2)+(5-7)^(2))/(5))`
`=sqrt((4+1+0+1+4)/(5)=sqrt(2))`
Hence, the least value of the standard deviation of 5 integers is `sqrt2`