If the variance σ 2 of the data x i 0 1 5 6 10 12 17 f i 3 2 3 2 6 3 3 is k then the value of k is ______ where . denotes the greatest integer funciton

Step-by-step solution

Finding the f i x i & f i x i 2 we get, Now, from above table we get, ∑ f i x i = 176 Now, finding x ¯ = ∑ f i x i ∑ f i = 176 22 = 8 Now, finding variance, we get, σ 2 = 1 N ∑ f i x i - 2 ( x ¯ ) 2 ⇒ σ 2 = 1 22 × 2048 - ( 8 ) 2 ⇒ σ 2 = 93 . 090964 ⇒ σ 2 = 29 . 0909 ⇒ σ 2 = 29 . 0909 = 29