Consider the statistics of two sets of observations as follows: Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the variance of the combined set of these two observations is 17 9 , then the value of n is equal to ________.

Step-by-step solution

σ 2 = n 1 σ 1 2 + n 2 σ 2 2 n 1 + n 2 + n 1 n 2 n 1 + n 2 x ¯ 1 - x ¯ 2 2 n 1 = 10 , n 2 = n , σ 1 2 = 2 , σ 2 2 = 1 x ¯ 1 = 2 , x ¯ 2 = 3 , σ 2 = 17 9 17 9 = 10 × 2 + n n + 10 + 10 n ( n + 10 ) 2 3 - 2 2 ⇒ 17 9 = ( n + 20 ) ( n + 10 ) + 10 n ( n + 10 ) 2 ⇒ 17 n 2 + 1700 + 340 n = 90 n + 9 n 2 + 30 n + 200 ⇒ 8 n 2 - 20 n - 100 = 0 2 n 2 - 5 n - 25 = 0 ⇒ 2 n + 5 n - 5 = 0 ⇒ n = - 5 2 ↓ Rejected , 5 Hence n = 5