QJEEM20Ma8dab: JEE Main 2020 Mathematics - Class 11 JEEM20Ma8dab Solution: If ∑ i = 1 n ( x i − a ) = n and ∑ i = 1 n ( x i − a ) 2 = n a…

Question

Verified Solution • 2025–26 Session moderate

If

\sum_{i = 1}^{n} (x_{i} - a) = n

and

\sum_{i = 1}^{n} {(x_{i} - a)}^{2} = n a

(n, a > 1) then the standard deviation of n
observations x₁ , x₂ , ..., x_n is :

Accepted Answer

S.D =

\sqrt{\frac{\sum_{i = 1}^{n} (x_{i} - a)}{n} - {(\frac{\sum_{i = 1}^{n} (x_{i} - a)}{n})}^{2}}

=

\sqrt{\frac{n a}{n} - {(\frac{n}{n})}^{2}}

=

\sqrt{a - 1}

Step-by-Step Verified Solution