The standard deviation of n observations ${x_1},{x_2}, \ldots ..,{x_n}\;$ is 2. If $\;\mathop \sum \limits_{i = 1}^n {x_i} = 20\;and\;\mathop \sum \limits_{i = 1}^n x_i^2 = 100$, then n is

JEE MATHEMATICS MCQ: STATISTICS

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Application +4 | -1

The standard deviation of n observations

{x_1},{x_2}, \ldots ..,{x_n}\;

is 2. If

\;\sum \limits_{i = 1}^n {x_i} = 20\;and\;\sum \limits_{i = 1}^n x_i^2 = 100

, then n is

View answer and explanation

Correct option: C

5\;\mathrm{ }or\;\mathrm{ }20

Option C (5 or 20) is correct because these are the possible values of n that satisfy the given conditions for the standard deviation and sums.

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{x_1},{x_2}, \ldots ,{x_n}

\bar X,

{x_i} + 2\;i;i = 1,\;2, \ldots ,n

1,3,5, x, y

-2,