The mean and variance of 5 observations are 6 and 6.8 respectively. If a number equal to mean is included in the set of observations and the variance of 6 observations is k , then the value of 34 k is equal to

Step-by-step solution

Let 5 observations are x 1 , x 2 , x 3 , x 4 , x 5 x ¯ old = 6 = x 1 + x 2 + x 3 + x 4 + x 5 5 ⇒ x 1 + x 2 + x 3 + x 4 + x 5 = 30 ... 1 Var . old = x 1 2 + x 2 2 + . . . . x 5 2 5 - x ¯ old 2 = 6.8 = x 1 2 + x 2 2 + . . . . x 5 2 = 214 ... 2 An observation 6 is included x ¯ new = x 1 + x   + x 3 + x 4 + x 5 + 6 6 = 6 x 1 2 + x 2 2 + x 3 2 . . . . x 5 2 + 6 2 = 214 + 36 = 250 Var . n e w = 250 6 - 6 2 = 34 6