# 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.

 x51015202530 f457432

Solution :

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

Take the assumed mean A = 15

 x51015202530Total f457432N  =  25 d  =  x - A-10-5051015 fd-40-250203030∑fd  =  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.

 Marks 65707580859095100 Number of students6113547104

Solution :

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

Take the assumed mean A = 80

 x65707580859095100Total f6113547104N  =  50 d  =  x - A-15-10-505101520 fd-90-110-150207015080∑fd  =  115

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

 Age (in years)131415161718 Number of students3891163

Solution :

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

Take the assumed mean A = 16

 x131415161718Total f3891163N  =  40 d  =  x - A-3-2-1012 fd-9-16-9066∑fd  =  -22

Arithmetic mean  =  A + [∑fd / N]

=  16 + (-22/40)

=  16 - 0.55

=  15.45

Example 4 :

Calculate the Arithmetic mean of the following data:

 x1525354555657585 f12201514161178

Solution :

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

Take the assumed mean A = 45

 x1525354555657585Total f12201514161178N  =  103 d  =  x - A-30-20-10010203040 fd-360-400-1500160220210320∑fd  =  0

Arithmetic mean  =  A + [∑fd / N]

=  45 + (0/103)

=  45 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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