If the variance of the following frequency distribution:
Class: $10 - 20 20 - 30 30 - 40$
Frequency: $2 x 2$
is $50,$ then $x$ is equal to _______

Question

If the variance of the following frequency distribution: Class: 10 - 20 20 - 30 30 - 40 Frequency: 2 x 2 is 50 , then x is equal to _______

TestHub · Accepted Answer

Given data can also be expressed as: x i 15 25 35 f i 2 x 2 So, x ¯ = ∑ f i x i Σ f i = 30 + 25 x + 70 4 + x = 25 4 + x 4 + x = 25 Now, σ 2 = 50 = ∑ f i x i 2 Σ f i - x ¯ 2 50 = 450 + 625 x + 2450 4 + x - 25 2 ⇒ 50 = 2900 + 625 x 4 + x - 625 ⇒ 675 ( 4 + x ) = 2900 + 625 x ⇒ 50 x = 200 ⇒ x = 4

Mathematics - Statistics Question with Solution | TestHub

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