Step deviation method — lesson. Mathematics CBSE, Class 10.

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Let us consider the steps for finding the mean of grouped data using the step deviation method.

Steps:

1. Calculate the midpoint of the class interval and name it as

$x_i$ .

2. From the data of

$x_i$ , choose any value(preferably in the middle) as the assumed mean(

$a$ ).

3. Determine the deviation (

$d = x_i - a$ ) for each class.

4. Determine the deviation (

$u = \frac{x_i - a}{h}$ where

$h$ is the class size) for each class.

5. Multiply the frequency and

$u_i$ of each class interval and name it as

$f_iu_i$ .

6. Calculate the mean by applying the formula

$\overline X = a + \left[\frac{\sum fd}{\sum f} \times h \right]$ .

Example:

Find the mean of the following frequency distribution:

Class interval	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$124$	$156$	$200$	$10$	$10$

Solution:

Let the assumed mean be

$a = 55$ and class width

$h = 10$ .

We know that the mean of the grouped frequency distribution using the step deviation method can be determined using the formula,

$\overline X = a + \left[\frac{\sum f_iu_i}{\sum f_i} \times h \right]$ .

Substituting the known values in the above formula, we have:

$\overline X = 55 + \left[\frac{-374}{500} \times 10 \right]$

$\overline X = 55 - 7.48$

$\overline X = 47.52$

Therefore, the mean of the given data is

$47.52$ .

Did you find an error?

6. Step deviation method