Q. For a statistical data $x_1,x_2,\dots,x_{10}$ of 10 values, a student obtained the mean as $5.5$ and $\sum_{i=1}^{10}x_i^2=371$. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is
A) $9$
B) $5$
C) $7$
D) $4$
Explanation
[Solution by Dr. Abubacker] $\sum x=55$ originally; corrected $\sum x=55-9+14=60$, mean $=6$. $\sum x^2=371-16-25+36+64=430$. Variance $=\frac{430}{10}-6^2=43-36=7$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.