The outcome of each of 30 items was observed; 10 items gave an outcome 1 2 - d each, 10 items gave outcome 1 2 each and the remaining 10 items gave outcome 1 2 + d each. If the variance of this outcome data is 4 3 then | d | equals:

Step-by-step solution

Outcomes are ( 1 2 -d ), ( 1 2 -d ), 0 , 10 times, 1 2 , 1 2 , , 10 times, 1 2 +d, 1 2 +d, , 10 times Mean = 1 30 ( 1 2 30 )= 1 2 Variance of the outcomes is, aligned ² &= 1 30 x_ i ²-( x )² &= 1 30 [ ( 1 2 -d )² 10+ ( 1 2 )² 10+ ( 1 2 +d )² 10 ]- 1 4 & 4 3 = 1 30 [30 1 4 +20 d² ]- 1 4 & 4 3 = 1 4 + 2 3 d²- 1 4 & d²=2 |d|= 2 aligned