JEE Main 2025 (Online) 7th April Morning ShiftQuestion 1
The mean and standard deviation of $100$ observations are $40$ and $5.1$, respectively. By mistake one observation is taken as $50$ instead of $40$. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $10(\mu+\sigma)$ is equal to
Statistics
Solution
Original sum $=4000$ (with $50$ counted); correct sum $=4000-50+40=3990$, so $\mu=39.9$. Wrong $\sum x^2=100(5.1^2+40^2)=162601$; correct $=162601-2500+1600=161701$. $\sigma^2=1617.01-39.9^2=1617.01-1592.01=25$, $\sigma=5$. $10(\mu+\sigma)=449$. Option B.