Question

There is a grouped data distribution for which mean is to be found by step deviation method.

A = assumed mean

B = class interval

C = sum of products of ‘u’ and frequency for each class interval

D = Total number of observations

Which of the following statements is true regarding mean(m) for the grouped distribution ?

• A. m = A + (C/D)
• B. m= A + B(C/D)
• C. m= A + D(B/C)
• D. m= A + (B/C)

Answer 1

The correct option is B

m= A + B(C/D)

The formula for mean by step deviation method is given below.

$\overline{x}$ = a + h$($ $\frac{\sum f_i{u}_i}{\sum f_i}$ $)$

Here a = assumed mean = A

h = class interval = B

$f_i$ = frequency of $i^{th}$ class

$u_i$ = $\frac{d_i}{h}$

$d_i$ = $x_i$ – a
$\sum f_i{u}_i$ = sum of products of ‘u’ and frequency for each class interval = C
D= total number of observation =$\sum f_i$
Hence m = A + B $\times$ $\frac{C}{D}$