Question

What is step-deviation method explain with an example?

Answer 1

Step 1: Mean

Mean is an arithmetic measure of a given data set that can be determined by dividing the sum of all data points by the number of data points in a given data set. In a data set, the average point of all the data points we have in the set.

$\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}$

Depending on the size of the data, there are three ways to find the meaning of data collected, such as

1. Direct Method
2. Assumed Mean Method
3. Step-deviation Method

Step-deviation Method

If the data values ​​are large, a step deviation method is used to obtain the definition. The formula is provided by:

Mean

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

Here,

1. $a=$ assumed mean
2. $f_i=$ frequency of ith class
3. $x_i–a=$ deviation of ith class

$u_i=\frac{(x_i–a)}{h}$

$\Sigma f_i=N=$ Total number of observations

$xi=$ class mark $=\frac{(\text{upper class limit}+\text{lower class limit})}{2}$

Step 2: Example

Find the mean of the following data set.

$10,20,36,12,35,40,36,30,36,40$

$\begin{array}{r}{x}_i=10,20,36,12,35,40,36,30,36,40\end{array}$

$n=10$

$\begin{array}{c}\text{Mean}=\sum x_i/n\\ =\frac{(10+20+36+12+35+40+36+30+36+40)}{10}\\ =\frac{295}{10}\\ =29.5\end{array}$

Therefore, the mean of the given data set is $29.5$.