Let sets and have elements each. Let the mean of the elements in sets and be and respectively, and the variance of the elements in sets and be and respectively. A new set of elements is formed by subtracting from each element of and adding to each element of . Then the sum of the mean and variance of the elements of is

38 Explanation: Given, Set and have elements each. Mean of , variance of Mean of , variance of After transformation: Each element of is replaced by New mean of Variance remains same Each element of is replaced by New mean of Variance remains same Now set has elements (5 from modified and 5 from modified ). Mean of : Variance of combined data: Sum of mean and variance of set :

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively, and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively. A new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding $2$ to each element of $B$ . Then the sum of the mean and variance of the elements of $C$ is

JEE 2023 — Mathematics PYQ

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