The mean of the following frequency distribution is 50 but the frequencies f₁ and f₂ in classes 20 - 40 and 60 - 80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.

Question

Philoid · Accepted Answer

First, we calculate the class mark of given data

Given that, sum of all frequencies = 120

Here,

assumed mean, a = 50 and

class width, h = 20

By step deviation method,

⇒ 4 + f₂ - f₁ = 0

⇒ -f₂ + f₁ = 4 - - - - (ii)

On adding Eqs. (i) and (ii), we get

2f₁ = 56

⇒ f₁ = 28

Put the value of in Eq. (i), we get

f₂ = 52 - 28

⇒ f₂ = 24

Hence, f₁ = 28 and f₂ = 24

The mean of the following frequency distribution is 50 but the frequencies f1 and f2 in classes 20 - 40 and 60 - 80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.

The mean of the following frequency distribution is 50 but the frequencies f₁ and f₂ in classes 20 - 40 and 60 - 80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.