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In Statistics Mean, Median and Mode are known as the measures of central tendencies.

The mean of a given data is given by the sum of values of all the given observations divided by the number of observations.

Mean of a given data ($\stackrel{\_}{\text{x}}$)= $\frac{\text{The sum of values of all given observations}}{\text{The number of observations}}$.

There are three methods to find the mean of a grouped data are:

**Direct method:**

Mid-point or Class mark (x_{i}) = $\frac{\text{[ Upper class limit + Lower class limit]}}{\text{2}}$

Mean of a given data using direct method ($\stackrel{\_}{\text{x}}$) =_{ }$\frac{\xe2\u02c6\u2018\text{f i x i}}{\xe2\u02c6\u2018\text{f i}}$_{ } .

Where f_{i} is frequency of the given class interval.

**Assumed Mean Method:**

Mean of grouped data using assumed mean method ($\stackrel{\_}{\text{x}}$) = A + $\frac{\xe2\u02c6\u2018\text{f i d i}}{\xe2\u02c6\u2018\text{f i}}$

Where d_{i} = x_{i} - A.

A is an Assumed Mean.

f_{i} is frequency of the given class interval.

d_{i} is Deviation of the assumed mean from a class mark.

**Step-deviation Method:**

Mean of grouped data using step-deviation method ($\stackrel{\_}{\text{x}}$) = A + h [ $\frac{\xe2\u02c6\u2018\text{f i u i}}{\xe2\u02c6\u2018\text{f i}}$]

Where u_{i} = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$

A is an Assumed Mean.

f_{i} is frequency of the given class interval.

h is class size.

The mean of a given data is given by the sum of values of all the given observations divided by the number of observations.

Mean of a given data ($\stackrel{\_}{\text{x}}$)= $\frac{\text{The sum of values of all given observations}}{\text{The number of observations}}$.

There are three methods to find the mean of a grouped data are:

- Direct Method
- Assumed Mean Method
- Step-deviation Method

Mid-point or Class mark (x

Mean of a given data using direct method ($\stackrel{\_}{\text{x}}$) =

Where f

Mean of grouped data using assumed mean method ($\stackrel{\_}{\text{x}}$) = A + $\frac{\xe2\u02c6\u2018\text{f i d i}}{\xe2\u02c6\u2018\text{f i}}$

Where d

A is an Assumed Mean.

f

d

Mean of grouped data using step-deviation method ($\stackrel{\_}{\text{x}}$) = A + h [ $\frac{\xe2\u02c6\u2018\text{f i u i}}{\xe2\u02c6\u2018\text{f i}}$]

Where u

A is an Assumed Mean.

f

h is class size.

- The step deviation method is more suitable, if the deviations of the class marks from the assumed mean are larger.
- In step-deviation method, the mean of grouped data remains the same for any non-zero numbers and , such that u
_{i}= $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$.

In Statistics Mean, Median and Mode are known as the measures of central tendencies.

The mean of a given data is given by the sum of values of all the given observations divided by the number of observations.

Mean of a given data ($\stackrel{\_}{\text{x}}$)= $\frac{\text{The sum of values of all given observations}}{\text{The number of observations}}$.

There are three methods to find the mean of a grouped data are:

**Direct method:**

Mid-point or Class mark (x_{i}) = $\frac{\text{[ Upper class limit + Lower class limit]}}{\text{2}}$

Mean of a given data using direct method ($\stackrel{\_}{\text{x}}$) =_{ }$\frac{\xe2\u02c6\u2018\text{f i x i}}{\xe2\u02c6\u2018\text{f i}}$_{ } .

Where f_{i} is frequency of the given class interval.

**Assumed Mean Method:**

Mean of grouped data using assumed mean method ($\stackrel{\_}{\text{x}}$) = A + $\frac{\xe2\u02c6\u2018\text{f i d i}}{\xe2\u02c6\u2018\text{f i}}$

Where d_{i} = x_{i} - A.

A is an Assumed Mean.

f_{i} is frequency of the given class interval.

d_{i} is Deviation of the assumed mean from a class mark.

**Step-deviation Method:**

Mean of grouped data using step-deviation method ($\stackrel{\_}{\text{x}}$) = A + h [ $\frac{\xe2\u02c6\u2018\text{f i u i}}{\xe2\u02c6\u2018\text{f i}}$]

Where u_{i} = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$

A is an Assumed Mean.

f_{i} is frequency of the given class interval.

h is class size.

The mean of a given data is given by the sum of values of all the given observations divided by the number of observations.

Mean of a given data ($\stackrel{\_}{\text{x}}$)= $\frac{\text{The sum of values of all given observations}}{\text{The number of observations}}$.

There are three methods to find the mean of a grouped data are:

- Direct Method
- Assumed Mean Method
- Step-deviation Method

Mid-point or Class mark (x

Mean of a given data using direct method ($\stackrel{\_}{\text{x}}$) =

Where f

Mean of grouped data using assumed mean method ($\stackrel{\_}{\text{x}}$) = A + $\frac{\xe2\u02c6\u2018\text{f i d i}}{\xe2\u02c6\u2018\text{f i}}$

Where d

A is an Assumed Mean.

f

d

Mean of grouped data using step-deviation method ($\stackrel{\_}{\text{x}}$) = A + h [ $\frac{\xe2\u02c6\u2018\text{f i u i}}{\xe2\u02c6\u2018\text{f i}}$]

Where u

A is an Assumed Mean.

f

h is class size.

- The step deviation method is more suitable, if the deviations of the class marks from the assumed mean are larger.
- In step-deviation method, the mean of grouped data remains the same for any non-zero numbers and , such that u
_{i}= $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$.