devarshi-dt-logo

Question:

The outcome of each of 30 items was observed; 10 items gave an outcome 12 - d each, 10 items gave outcome 12 each and the remaining 10 items gave outcome 12 + d each. If the variance of this outcome data is 43, then |d| equals:

2

23

√2

√52

Solution:

The correct option is D √2
Variance is independent of origin. So we shift the given data by 12.
so, 10d^2 + 10 × 0^2 + 10d^2 / 30 - (0)^2 = 43
⇒ d^2 = 2
⇒ |d| = √2