If the mean of the frequency distribution Class : 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency : 2 3 x 5 4 is 28 , then its variance is ________ .

Step-by-step solution

Given that the mean for the frequency distribution is 28 . We know that Mean x = ∑ f i x i ∑ f i Now for the class interval 0 - 10 we get x 1 = 0 + 10 2 = 5 . Similarly we can calculate x i for other class intervals. Now we know that mean = 28 ⇒ 2 × 5 + 3 × 15 + x × 25 + 5 × 35 + 4 × 45 14 + x = 28 ⇒ x = 6 Also we know that variance σ 2 = ∑ f i x ¯ - x i 2 ∑ f i σ 2 = 2 × 28 - 5 2 + 3 × 28 - 15 2 + 6 × 28 - 25 2 + 5 × 28