HOW TO FIND THE MISSING NUMBER OF ARITHMETIC MEAN

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 x̄  =  (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 x̄ 

=  (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

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