Mean of Grouped Data


 
 
Concept Explanation
 

Mean of Grouped  Data

Mean Of Grouped  Data:

Grouped data is data that has been grouped together in categories. Mean of a set of observations is the average of the given observations. To find the mean, we divide the sum of the observations by the total number of observations. However, for grouped data, we cannot find the exact Mean, we can only give estimates.

There are three methods for finding the mean from a grouped frequency table.

1.  Mean Using Class Mark.

2. Assumed Mean Method

3. Step Deviation Method

Mean of Grouped  Data Using Class Mark:

The mean (or average) of observations, as we know , is the sum of the values of all the observations divided by the total number of observations. For grouped data we will find the class mark for each class and denote it with  large x_{1},x_{2}....,x_{n} for the respective class with frequencies large f_{1},f_{2}....,f_{n}, In other way we say that the frequency denotes the number times  the class mark is occurring. That is why the mean calculated using grouping is not accurate but is an estimate.

Now, the sum of the values of all the observations

=f_{1}x_{1}+f_{2}x_{2}+...+f_{n}x_{n},

and the number of observations

=f_{1}+f_{2}+...+f_{n}   

So, the mean large bar{x} of the data is given by

                                      bar{x}=frac{f_{1}x_{1}+f_{2}x_{2}+...+f_{n}x_{n}}{f_{1}+f_{2}+...+f_{n}}

                                      bar{x}=frac{sum_{i=1}^{n}f_{i}x_{i}}{sum_{i=1}^{n}f_{i}}

Illustration: Find the mean of the following data:

Class interval 10-25 25-40 40-55 55-70 70-85 85-100
Number of students 2 3 7 6 6 6

Solution

Class interval Number of students (f_{i}) Class mark (x_{i}) large f_{i}x_{i}

10-25

25-40

40-55

55-70

70-85

85-100

2

3

7

6

6

6

17.5

32.5

47.5

62.5

77.5

92.5

35.0

97.5

332.5

375.0

465.0

555.0

Total sum f_{i}=30   sum f_{i}x_{i}=1860.0
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Sample Questions
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Question : 1

Find the mean of grouped data can be calculated using __________________ . 

 

Right Option : D
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Explanation
Question : 2

Find the mean of the following distribution. 

Class Interval 0 - 20 20 - 40 40 - 60 60 - 80
fi 5 11 10 4

 

Right Option : B
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Explanation
Question : 3

Find the mean of the following distribution. 

Class Interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
fi 8 7 10 2 3

 

Right Option : C
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Explanation
 
 


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