If ui = (xi - 25)/10, Σ fiui = 20, Σ fi = 100, then bar x = A. 23, B. 24. C. 27 D. 25

Question

If \(u_i=\frac{Xi-25}{10},\) \(\sum f_iu_i=20,\sum f_i=100,\) then \(\bar{X}=\)

A. 23 

B. 24 

C. 27 

D. 25

Answer 1

We have given,

\(\sum f_iu_i = 20\)

Also,

\(u_i=\frac{X_i-25}{10}\)

Putting this in above equation

Now, given \(\sum f_i=100...[1]\)

using this

We have,

We know,

If x₁, x₂, … , x_n are observations with frequencies f₁, f₂, … , f_n i.e. x₁ occurs f₁ times and x₂ occurs f₂ times and so on, then mean \((\bar{X})\) of observations is given by

\(\bar{X}=\frac{\sum f_iX_i}{\sum f_i}\)

From [1] and [2]

\(\bar{X}=\frac{2700}{100}=27\)