Statistics
Mean and Variance
IIT-JEE 2005
Grade 11
Question:
The mean and variance of 8 observations are 9 and 9.25 respectively. If six of these observations are 6, 7, 10, 12, 12, 13, then the remaining two observations are:
(1) 5 and 7
(2) 4 and 8
(3) 3 and 9
(4) 6 and 6
Step-by-Step Solution
Key Concept: Use $\sum x_i = 8\bar{x}$ to find the sum of the two missing observations, and $\text{Var} = \frac{1}{8} \sum x_i^2 - \bar{x}^2$ to find the sum of their squares — then solve the resulting pair of equations.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)