Let the observations ${x_i}\left( {1 \le i \le 10} \right)$ satisfy the equations, $\sum\limits_{i = 1}^{10} {\left( {{x_i} - 5} \right) = 10} $ and $\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - 5} \right)}^2} = 40.} $ If $\mu $ and $\lambda $ are the mean and the variance of the observations, ${x_1} - 3,\,{x_2} - 3,.....,{x_{10}} - 3,$ then the ordered pair $\left( {\mu ,\lambda } \right)$ is equal to

JEE MATHEMATICS MCQ: STATISTICS

1 Easy

1 of 1

Application +4 | -1

Let the observations

{x_i}\left( {1 \le i \le 10} \right)

satisfy the equations,

\sum\limits_{i = 1}^{10} {\left( {{x_i} - 5} \right) = 10}

and

\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - 5} \right)}^2} = 40.}

\mu

and

\lambda

are the mean and the variance of the observations,

{x_1} - 3,\,{x_2} - 3,.....,{x_{10}} - 3,

then the ordered pair

\left( {\mu ,\lambda } \right)

is equal to

View answer and explanation

Correct option: C

(3,3)

Option C (3,3) is correct because it accurately calculates the mean and variance of the transformed observations based on the given data.