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.

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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 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 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,

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.

Combined mean

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

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,

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,

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,

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,

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