# HOW TO FIND THE MISSING NUMBER OF ARITHMETIC MEAN

## About "How to find the missing number of arithmetic mean"

How to find the missing number of arithmetic mean :

Here we are going to see how to find the missing number of arithmetic mean.

To find the missing observation from the group of observation, we have to use the formula given below.

Average

=  Sum of observations / Total number of observations

The following example problems will show you the method of finding missing number from the group of observations.

Example 1 :

If the average of the values 9, 6, 7, 8, 5 and x is 8. Find the value of x.

Solution :

Here, the given values are 9, 6, 7, 8, 5 and x, also n = 6.

By formula, A.M   =  (9 + 6 + 7 + 8 + 5 + x) / 6

(35 + x) / 6  =  8

Multiply 6 on both sides

35 + x = 48

x = 48 – 35 = 13

Hence the missing observation is 13.

Example 2 :

If the average of the values 18, 41, x , 36, 31, 24, 37, 35, 27, 36, is 31. Find the value of x.

Solution :

Here, the given values are 18, 41, x , 36, 31, 24, 37, 35, 27, 36, is 31 and n  =  10

By formula, A.M

=  (18 + 41 + x + 36 + 31 + 24 + 37 + 35 + 27 + 36 ) / 10

(285 + x) / 10  =  31

Multiply 10 by both sides

285 + x  =  310

x = 310 – 285  =  25

Hence the missing observation is 25.

Example 3 :

If in a class of 20 students, 5 students have scored 76 marks, 7 students have scored 77 marks and 8 students have scored 78 marks, then compute the mean of the class.

Solution :

Mean  =  Sum of marks of 20 students / 20

5 students have scored 76 marks

7 students have scored 77 marks

8 students have scored 78 marks

=  [ 5 (76) + 7 (77) + 8 (78) ] / 20

=  (380 + 539 + 624) / 20

=  1543 / 20

=  77.15 After having gone through the stuff given above, we hope that the students would have understood "How to find the missing number of arithmetic mean".

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