Chapter 13 · Question 3

When is the step-deviation method useful? State its formula.

Answer

It is useful when class marks have a common factor in their deviations. Let

u_i=\frac{x_i-a}{h}

. Then

\bar{x}=a+h\frac{\sum f_i u_i}{\sum f_i}

.

Divide deviations by class width to make numbers smaller.

If all

d_i=x_i-a

are multiples of a common number

h

, define

u_i=\frac{d_i}{h}

. Then the mean is

\bar{x}=a+h\frac{\sum f_i u_i}{\sum f_i}

. This simplifies arithmetic for large grouped data.