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
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