Question

Out of 30 observations, 10 observation is (1/2 - d), 10 observations are 1/2, and the remaining 10 observations is (1/2 +d). if the variance of 30 observations is 4/3 then |d| is equal to?

Answer 1

it has given that, Out of 30 observations, 10 observation is (1/2 - d), 10 observations are 1/2, and the remaining 10 observations is (1/2 +d).

To find : if the variance of 30 observations is 4/3 then |d| is equal to...

solution : using variance formula,

$\quad\sigma^2=\frac{\Sigma x_i^2}{N}-\bar{x}^2$

here, variance, σ² = 4/3

so, 4/3 = [10(1/2 - d)² + 10(1/2)² + 10(1/2 + d)²]/30 - [{10(1/2 - d) + 10(1/2) + 10(1/2 + d)}/30]²

⇒4/3 = [(1/4) + (d)² + (1/4) + (1/4) + (d)²]/3 - (1/2)²

⇒4/3 = 1/4 + 2d²/3 - 1/4

⇒4/3 = 2d²/3

⇒d² = 2

⇒|d| = √2

Therefore the value of |d| = √2

Answer 2

Answer:

d= $\sqrt{2}$