FIND ARITHMETIC MEAN BY ASSUMED MEAN METHOD

Formula to find arithmetic mean for a grouped data using assumed mean : 

=  A + [∑fd / N]

Here A is the assumed mean. 

Example 1 :

Calculate arithmetic mean for the following data. 

Solution :

Now we have to use the formula given above to find the arithmetic mean.

Take the assumed mean A = 15

Arithmetic mean  =  A + [∑fd / N] 

=  15 + (15/25)

=  15 + (3/5)

=  (75 + 3)/5

=  78/5

=  15.6

Example 2 :

Calculate arithmetic mean for the following data. 

Solution :

Now we have to use the formula given above to find the arithmetic mean.

Take the assumed mean A = 80

Arithmetic mean  =  A + [∑fd / N] 

=  80 + (115/50)

=  80 + (23/10)

=  80 + 2.3

=  82.3

Example 3 :

The following data give the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students

Solution :

Now we have to use the formula given above to find the arithmetic mean.

Take the assumed mean A = 16

Arithmetic mean  =  A + [∑fd / N] 

=  16 + (-22/40)

=  16 - 0.55

=  15.45

Example 4 :

Calculate the Arithmetic mean of the following data:

Solution :

Now we have to use the formula given above to find the arithmetic mean.

Take the assumed mean A = 45

Arithmetic mean  =  A + [∑fd / N]

=  45 + (0/103)

=  45

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