Statistics
Correction of Data / Variance
nta_pyq_2025_apr
Grade 11
Question:
For a statistical data $x_1, x_2, \ldots, x_{10}$ 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 incorrect values and adding correct ones, then recompute variance.
New $\sum x_i = 55 - (4+5) + (6+8) = 60$. New $\sum x_i^2 = 371 - (4^2+5^2) + (6^2+8^2) = 430$. $\sigma^2 = \frac{430}{10} - \left(\frac{60}{10}\right)^2 = 43 - 36 = 7$.
Correct Answer: 7