Question

For a set of 500 observations variance is found to be 125. If 25 is added to each observation and 55 is subtracted then the new variance under simplification?

Answer 1

Answer:

Variance remain same in each case

= 125

Step-by-step explanation:

Variance  = (1/n) ∑ (xi  _ mean)²

500 observations variance is found to be 125

=> 125  = (1/500) ∑ (xi  _ mean)²

Mean = (1/n) ∑ xi

Case1 :

if 25 is added to each observation

then New Mean Would be (∑ xi  + 25n )/n  = old Mean + 25

each Value would be xi + 25

Mean will be old mean + 25

Hence

Variance Would remain Same

= 125

Similarly in case 2

When 55 is subtracted

mean will be reduced by 55

but Variance remain same = 125