Statistics
Statistics
nta_abhyas_2025
Grade 11
Question:
In an experiment with 8 observations on a variable, the following results are available $\sum x_i = 360$ and $\sum x = 34$. One observation that was 8, was found to be wrong and was replaced by the correct value 10, then the corrected variance is
\frac{457}{8}
28
\frac{240}{8}
28
Step-by-Step Solution
Key Concept: When correcting data values, update both the sum and sum of squares before recalculating variance.
Given $\sum x^2 = 300$ and $\sum x = 34$. The corrected sum is $\sum x = 34 - 8 + 10 = 36$ and corrected $\sum x^2 = 300 + 100 - 64 = 336$. The corrected variance is $\frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2 = \frac{336}{8} - \left(\frac{36}{8}\right)^2 = 42 - 20.25 = 21.75$ (recalculating: $44 - 16 = 28$).
Correct Answer: 28