The first of the two samples in a group has 100 items with mean 15 and standard deviation 3 . If the whole group has 250 items with mean 15 . 6 and standard deviation 13 . 44 , then the standard deviation of the second sample is:

Step-by-step solution

We have, number of terms in the first group n 1 = 100 with their mean X 1 = 15 and number of terms in whole group is n 1 + n 2 = 250 and their mean X = 15 . 6 . Variance of first group V 1 x = 9 and whole group is Var x = 13 . 44 . Now, σ 2 = n 1 σ 1 2 + n 2 σ 2 2 n 1 + n 2 + n 1 n 2 n 1 + n 2 2 x ¯ 1 - x ¯ 2 2 and n 2 = 150 , x ¯ 2 = 16 , V 2 ( x ) = σ 2 Therefore, 13 . 44 = 100 × 9 + 150 × σ 2 2 250 + 100 × 150 250 2 × 1 ⇒ σ 2 2 = 16 ⇒ &