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Mean of Grouped Data

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Mean of Grouped Data - Lesson 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 ( x _ )=  The sum of values of all given observations 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 (x i) = [ Upper class limit + Lower class limit] 2

Mean of a given data using direct method ( x _ ) = ∑ f i x i ∑ f i   .

Where f i is frequency of the given class interval.

Assumed Mean Method:

Mean of grouped data using assumed mean method ( x _ ) = A + ∑ f i d i ∑ 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 ( x _ ) = A + h [ ∑ f i u i ∑ f i ]

Where u i = x i - A h

A is an Assumed Mean.

f i 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 = x i - A h .

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