Arithmetic Mean (Average)

Arithmetic Mean (Average)


Arithmetic Mean (Average)

Arithmetic Mean (Average) is the measure of single central value or average of the given data that represents the characteristics of entire data. Arithmetic Mean (Average) is given by dividing the sum of all data by the total number of data.

Arithmetic mean (Average) for individual data:

Arithmetic mean or average for individual data is given by dividing the total sum of data by the total number of data. i.e.
Arithmetic mean (Average) for individual data
                  

Arithmetic mean (Average) for discrete data:

A data having some repeated value i.e. frequency is called discrete data. To calculate the mean of repeated data, we follow the following steps:

1.  Draw a table with 3 columns.
2.  Write down the items (x) in ascending order in the first column.
3.  Write the corresponding frequency (f) of each item in the second column.
4.  Find the product of each item (x) and its frequency (f) in the third column.
5.  Find the total of f column and fx column.
6.  Divide the sum of fx by the sum of f i.e. N to get the mean. i.e.
Arithmetic mean (Average) for discrete data

Arithmetic mean (Average) for grouped data:

The data, which have class interval and frequency is called grouped data. To calculate the mean of grouped data, we follow the following steps:
1.  Draw a table with 4 columns.
2.  Calculate the mid-value (m) of each class interval by applying the formula,
mid-value (m)
3.  Write down the items (m) in ascending order in the second column.
4.  Write the corresponding frequency (f) of each item in the third column.
5.  Find the product of each item (m) and its frequency (f) in the fourth column.
6.  Find the total of f column and fm column.
7.  Divide the sum of fm by the sum of f i.e. N to get the mean. i.e.
Arithmetic mean (Average) for grouped data

Combined mean

We can compute a single mean from the means of different sets of data. Such mean is called combined mean.

Combined mean


Workout Examples

Example 1: Find the mean of data: 10, 70, 80, 40, 50, 60
Solution: Here,
                        Data: 10, 70, 80, 40, 50, 60
                        No. of data (N) = 6
                        Mean () = ?
We know,
mean for individual data



Example 2: Find the mean marks of:

Marks
10
20
30
40
50
No. of students
1
2
3
4
5

Solution: Here,
                      
Marks (x)
Frequency (f)
f × x
10
20
30
40
50
1
2
3
4
5
10
40
90
160
250

N = 15
∑fx = 550

Now,
mean for discrete data


Example 3: Find the value of m from the following data, if mean is 36.

Marks
10
20
38
40
50
No. of students
1
2
m
2
3

Solution: Here,    
      
Marks (x)
Frequency (f)
f × x
10
20
38
40
50
1
2
m
2
3
10
40
38m
80
150

N = 8+m
∑fx = 280+38m

Now,
mean for discrete data
or,        280+38m = 36(8+m)
or,        280+38m = 288+36m
or,        38m-36m = 288-280
or,        2m = 8
or,        m = 8/2
or,        m = 4

The value of m is 4.



Example 4: Find the mean of the following data:

Marks
10-20
20-30
30-40
40-50
50-60
No. of students
2
3
2
4
5

Solution: Here, 
                     
Marks
Mid-value (m)
Frequency (f)
f × m
10-20
20-30
30-40
40-50
50-60
15
25
35
45
55
2
3
2
4
5
30
75
70
180
275


N = 16
∑fx = 630

Now,
mean for grouped data


Example 5: The mean weight of 25 boys is 45.6kg and that of 32 girls is 39.9kg find their mean weight.

Solution: Here,
Example 5: Solution



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