Two data sets each of size 10 has the variance as 4 and k and the corresponding means as 2 and 4 respectively. If the variance of the combined data set is 5 ⋅ 5 , then the value of k is equal to

Step-by-step solution

Combined mean, x - = 2 × 10 + 4 × 10 20 = 3 d 1 = x 1 - - x - = - 1 d 2 = x 2 - - x - = 1 Combined variance = n 1 σ 1 2 + n 2 σ 2 + n 1 d 1 2 + n 2 d 2 2 n 1 + n 2 ⇒ 11 2 = 10 × 4 + 10 × k + 10 × 1 + 10 × 1 20 ⇒ k = 5