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 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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