5 students of a class have an average height 150 c m and variance 18 c m 2 . A new student, whose height is 156 c m , joined them. The variance i n c m 2 of the height of these six students is:

Step-by-step solution

Let 1 s t 5 students are x 1 , x 2 , x 3 , x 4 and x 5 ∴ 18 = E x 2 - E x 2 = x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 5 - 150 2 ⇒ x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 = 112590 ∴ new variance = x 1 2 + x 2 2 + . . . . + x 5 2 + 156 2 6 - ( 151 ) 2 S i n c e n e w m e a n = 150 × 5 + 156 6 = 151 = 112590 + 24336 6 - 22801 = 20