Statistics
Effect on variance when one observation is changed
nta_pyq_2023_jan
Grade None
Question:
The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to:
Step-by-Step Solution
Key Concept: From new mean: $\sum x_i - 8 + 12 = 10.2n$, and $\sum x_i = 10n$. Solve for $n$. Then update $\sum x_i^2$ and compute the new variance.
$n = 20$. $\sum x_i^2 = 2080$. After change: new $\sum x_i^2 = 2160$. New variance $= \frac{2160}{20} - (10.2)^2 = 108 - 104.04 = 3.96$.
Correct Answer: 3