Question

why does step deviation method is used for calculating mean in class 10 th?

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Answer 1

There are many ways by which you can calculate the mean of grouped data.

$\textbf{\huge{Direct Method}}$

Direct Method is mainly suitable for calculating the mean of small grouped data where numbers are not very large. It contains $x_{i}$(class mark) and $f_{i}$(frequency). The formula for calculating mean by Direct Method is:

$\tt \bar{x} = \dfrac{\Sigma \: x_{i}f_{i}}{ \Sigma \:f_{i} }$

$\textbf{\huge{Indirect Method}}$

Indirect Method is further divided into two sub-divisions. These are:

$\textbf{Assumed Mean}$

In this method, we chose a number from the class marks (middle number) and then apply $x_{i}-a$ to get $d_{i}$. This method is used usually when the numbers are somewhat bigger than those in the direct method. The formula for calculating mean by assumed mean method is:

$\tt \bar{x} = a + \dfrac{\Sigma \: f_{i} d_{i}}{ \Sigma\: f _{i} }$

$\textbf{Step Deviation}$

This is the method which is used when the numbers are very large and calculation becomes complicated. Here, a new value $u_{i}$ is introduced which is $\dfrac{d_{i}}{h}$ where h is the class size. The formula for calculating mean by step deviation method is:

$\tt \bar{x} = a + \dfrac{h \Sigma \: f_{i}u_{i} }{ \Sigma \: f _{i} }$

So, Why is Step Deviation method mainly used for calculating mean of grouped data?

This is because this method makes the calculation very simple by simplifying the large numbers. It is error free and accurate. This is the main reason why Step Deviation method is generally considered for calculating the mean of grouped data.

Answer 2

Question : Why does step deviation method is used for calculating mean in class 10th?

Step Deviation Method :

When the number of scores in a data is large, it becomes tedious to write all numbers in the formula and take their sum. So, we use some different methods to find the sum.

Sometimes, the large data collected from an experiment is presented in a table in grouped form. In such case, we can't find exact mean of the statistical data. Hence,  a method is used which gives the approximate mean or a number nearby.

Step Deviation Method is used to reduce the calculations further. Steps to calculate the mean by this method is as follows :

1. In Column 1, write the given class interval.

2. In Column 2, write the corresponding class marks.

3. In Column 3, write the values of di where di = xi - A.

4. Find g, the G. C. D of all di. In Column 4, write the values of ui, where,

$\tt{u_{i} =  \frac{ x_{i} -A}{g} =\frac{d _{i} }{g}}$

5. In Column 5, write the frequencies ( fi ) of the given class intervals. Also, Find their sums.

6. In Column 6, write fi ui. Find their sum and u, using the formula,

$\tt{ \bar{u} =\frac{ f_{i}{u_{i}}}{ \sum \: f_{i}}}$

Hence, Lastly Find the mean using last formula which is given below :

$\tt{ \bar {X} = A + \bar{u}g}$

Thus, Step Deviation Method is used to reduce the calculations still further.

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