Question

Explain the direct and shortcut method of discrete series for calculating arithmetic mean with example.

Answer 1

$\huge\mathfrak\pink{answer}$

Direct method :-

Formula

$x = \frac{sigma \: fx}{sigma \: f}$

Ex :-

Table →

Wages ( X). = 10 ; 20 ; 30 ; 40 ; 50

No. of workers (f) = 4. ; 5 ; 3. ; 2. ; 5

Multiple ( fx ) = 40 ; 100 ; 90 ; 80 ; 250

Sum (fx ) = 560

sum (f) = 19

$mean \: = \frac{560}{19} = 29.47$

Shortcut method

Formula

$x \: = a + \frac{sum \: of \: fd}{sum \: of \: f}$

Taking 1st examples table again

Deviation

Let A = 30

( d = x-A) = -20 ; -10 ; 0 ; 10 ; 20

Multiple (fd)= -80. ; -50 ;0.;20. ;100

$= 30 + ( - \frac{10}{19} ) \\ = 29.47$