Statistics
Mean Deviation about Mean — Finding α, β
nta_pyq_2024_apr
Grade 11
Question:
Let $\alpha,\beta\in\mathbb{R}$. Let the mean and the variance of 6 observations $-3,4,7,-6,\alpha,\beta$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:
$\dfrac{13}{3}$
$\dfrac{16}{3}$
$\dfrac{11}{3}$
$\dfrac{14}{3}$
Step-by-Step Solution
Key Concept: Mean $=2\Rightarrow\frac{-3+4+7-6+\alpha+\beta}{6}=2\Rightarrow\alpha+\beta=10$. Variance $=23\Rightarrow\frac{\sum x_i^2}{6}-\mu^2=23\Rightarrow\frac{9+16+49+36+\alpha^2+\beta^2}{6}=27\Rightarrow\alpha^2+\beta^2=52$.
$\alpha=4,\beta=6$. Mean deviation $=\frac{5+2+5+8+2+4}{6}=\frac{13}{3}$.
Correct Answer: 1