Statistics
Statistics
nta_pyq_2025_jan
Grade 11
Question:
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:
Step-by-Step Solution
Key Concept: Update $\sum x_{i}$ and $\sum x_{i}^{2}$ by removing the wrong values and adding the correct ones, then use $\sigma^{2}=\dfrac{\sum x_{i}^{2}}{n}-\bar{x}^{2}.$
$\sum x_{i}=5.5\cdot 10=55.$ Corrected $\sum x_{i}=55-(4+5)+(6+8)=60.$ New $\bar{x}=6.$
Corrected $\sum x_{i}^{2}=371-(16+25)+(36+64)=430.$
$\sigma^{2}=\dfrac{430}{10}-36=43-36=7.$
Correct Answer: 3