JEE Main 2022 (Online) 26th July Evening ShiftQuestion 1
The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38\sigma^2$ is equal to ________.
Statistics
Answer$238$
Solution
$\sum x=1200$, $\sum x^2=40(25+900)=37000$. Remove 12 and 10: $\sum x=1178$, $\sum x^2=37000-244=36756$, 38 observations. $38\sigma^2=\sum x^2-\frac{(\sum x)^2}{38}=36756-\frac{1178^2}{38}=36756-36518=238$.