JEE MATHEMATICS MCQ: STATISTICS

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\bar{x}

is the mean and

\sigma^2

is the variance of

n

observations

x_1, x_2, \ldots, x_n

, then which of the following are true for the observations

{ax}_1, {ax}_2,{ax}_3, \ldots, {ax}_n?

I. Mean of the observations is

\frac{\bar{x}}{{a}}

.

II. Variance of the observations is

\frac{\sigma^2}{{a}^2}

.

III. Mean of the observations is

a \bar{x}

.

IV. Variance of the observations is

a^2 \sigma^2

View answer and explanation

Correct option: D

III and IV are true

Option D (III and IV are true) is correct because multiplying each observation by a constant 'a' multiplies the mean by 'a' and the variance by a squared.

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