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

Example 4 :

A group of twenty had to complete the same test. Nineteen of them did it first and had an average of 35. The other pupil did the test a day later and scored 55. What is the average for this group of twenty ?

Solution :

Average of 19 people = 35

Sum of 19 people / 19 = 35

Sum of 19 people = 35 (19)

= 665

Score of 20th person = 55

Average of 20 people = (665 + 55)/20

= 720/20

= 36

Average of 20 people is 36.

Example 5 :

A group of eight pupils obtain scores on their spelling test of 15, 19, 23, 43, 47, 48, 50 and 51 ?

How many of them scored above the average ?

Solution :

15, 19, 23, 43, 47, 48, 50 and 51

Mean of above scores

= (15 + 19 + 23 + 43 + 47 + 48 + 50 + 51)/8

= 296/8

= 37

Average = 37

Scores above 37 are 43, 47, 48, 50 and 51

So, there are 5 students above the average.

Example 6 :

In a test out of 10, a group of pupils scored these marks.

6, 7, 9, 5, 4, 10, 8

a) What was the mean mark ?

b)  In a different test, a teacher calculated that the group of 12 pupils had scored an average of 24 marks (out of 30) on a test. However, the teacher had incorrectly marked one pupil's test giving him 13 out of 30 when he really should have got 19 out of 30. What should the correct average be ?

Solution :

a)  Given scores are 6, 7, 9, 5, 4, 10, 8

Average score = (6 + 7 + 9 + 5 + 4 + 10 + 8)/7

= 49/7

= 7

b)

Average of 12 pupil = 24

Sum of 12 people / 12 = 24

Sum of 12 people = 24(12)

= 288

Correct score = 19, wrongly entered as 13

Correct sum = 288 + 19 - 13

= 294

Correct average = 294/12

= 24.5

Example 7 :

Four grandchildren in a room are 2, 3, 5 and 10 years old. The mean age of the grandchildren in the room increases by 2 years when a fifth grandchild enters. How old is the fifth grandchild ?

Solution :

Sum of four grandchildren = 2 + 3 + 5 + 10

= 20

Mean age of 4 grandchildren = 20/4

= 5

Let x be the fifth grand child.

(2 + 3 + 5 + 10 + x)/5 = 5 + 2

(20 + x)/5 = 7

20 + x = 7(5)

20 + x = 35

x = 35 - 20

x = 15

So, age of fifth grandchild is 15 years old.

Example 8 :

The mean of two numbers is 12. One of the numbers is 10. What is the other number?

Solution :

Mean of two numbers = 12

One number = 10

Let x be the other number

(x + 10)/2 = 12

x + 10 = 12(2)

x + 10 = 24

x = 24 - 10

x = 14

So, the required number is 14.

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