JEE Main 2024 (Online) 29th January Evening ShiftQuestion 1
If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four observations is $\frac72$, then the variance of the first four observations is equal to
Statistics
Solution
Total $=24$, first four sum $=14$, so fifth $=10$. $\sum x^2=5\left(\frac{194}{25}+\frac{576}{25}\right)=154$, first four $\sum x^2=54$. Variance $=\frac{54}{4}-\left(\frac72\right)^2=\frac54$.