Question

equation of assumed mean

Answer 1

Hey friend,

There are three methods of finding mean,

•Direct method = Σfixi/Σfi

•Assumed mean method = a + Σfidi/Σfi

•Step deviation method or shortcut method = a + {Σfiμi/Σfi} × h

where

fi = frequencies

xi = class marks

Σfixi = Sum of frequencies and class marks

a = assumed mean

di = deviations

→ di = xi - a

Σfidi = sum of frequencies and deviations

μi = (xi - a)/h

h = class size

Assumed mean method derivation:-

Let đ = d bar

đ = Σfidi/Σfi

đ = {Σfi(xi - a)}/Σfi

{di = xi - a}

đ = Σfixi/Σfi – Σfia/Σfi

Let x† = x bar

đ = x† - a.Σfi/Σfi

đ = x† - a(1)

đ = x† - a

x† = đ+a

x† = Σfidi/Σfi + a

x† = a + Σfidi/Σfi

Thus derived.

Hope it helps