Notes On Mean of Grouped Data - CBSE Class 10 Maths
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 Assumed Mean Method Step-deviation Method Direct method: Mid-point or Class mark (xi) = $\frac{\text{[ Upper class limit + Lower class limit]}}{\text{2}}$ Mean of a given data using direct method ($\stackrel{_}{\text{x}}$) = $\frac{\sum \text{f i x i}}{\sum \text{f i}}$   . Where fi is frequency of the given class interval. Assumed Mean Method: Mean of grouped data using assumed mean method ($\stackrel{_}{\text{x}}$) = A + $\frac{\sum \text{f i d i}}{\sum \text{f i}}$ Where di = xi - A. A is an Assumed Mean. fi is frequency of the given class interval. di 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 [ $\frac{\sum \text{f i u i}}{\sum \text{f i}}$] Where ui = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$ A is an Assumed Mean. fi is frequency of the given class interval. 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 ui = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$.

#### Summary

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 Assumed Mean Method Step-deviation Method Direct method: Mid-point or Class mark (xi) = $\frac{\text{[ Upper class limit + Lower class limit]}}{\text{2}}$ Mean of a given data using direct method ($\stackrel{_}{\text{x}}$) = $\frac{\sum \text{f i x i}}{\sum \text{f i}}$   . Where fi is frequency of the given class interval. Assumed Mean Method: Mean of grouped data using assumed mean method ($\stackrel{_}{\text{x}}$) = A + $\frac{\sum \text{f i d i}}{\sum \text{f i}}$ Where di = xi - A. A is an Assumed Mean. fi is frequency of the given class interval. di 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 [ $\frac{\sum \text{f i u i}}{\sum \text{f i}}$] Where ui = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$ A is an Assumed Mean. fi is frequency of the given class interval. 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 ui = $\frac{{\text{x}}_{\text{i}}\text{- A}}{\text{h}}$.

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