Statistics
Observation Replacement — α+β
nta_pyq_2026_jan
Grade 11
Question:
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha+\beta$ equals
Step-by-Step Solution
Key Concept: Original: $\sum x_i=100$, $\sum x_i^2=1020$. After replacing: $\beta-\alpha=1\Rightarrow\beta=\alpha+1$. New $\sum x_i^2=1040$: $\beta^2-\alpha^2=20\Rightarrow(\beta-\alpha)(\beta+\alpha)=20$.
$\alpha+\beta=20$.
Correct Answer: 4