Let the mean of the data x 1 3 5 7 9 Frequency f 4 24 28 α 8 be 5 . If m and σ 2 are respectively the mean deviation about the mean and the variance of the data, then 3 α m + σ 2 is equal to _ _ _ _ _ _ _ .

Step-by-step solution

Given, The mean of the below data is 5 x 1 3 5 7 9 Frequency f 4 24 28 α 8 Now finding mean we get, 4 + 72 + 28 × 5 + 7 α + 72 64 + α = 5 ⇒ α = 16 So, total number of observation will be, ∑ f i = 80 Now finding, mean deviation we get, M . D = ∑ f i x i - 5 ∑ f i = 4 × 4 + 24 × 2 + 0 + 16 × 2 + 8 × 4 80 = 8 5 So, m = 8 5 Now finding, variance we get, σ 2 = ∑ f i x i - 5 2 ∑ f i ⇒ σ 2 = 4 × 16 + 24 × 4 + 0 + 16