(a) The mean of the numbers 6, y, 7, x, 14 is 8. Express y in terms of x.
(b) The mean of 9 variates is 11. If eight of them are 7, 12, 9, 14, 21, 3, 8, and 15 find the 9th variate.
Solution:
(a) Sum of numbers = 6 + y + 7 + x + 14
= 27 + x + y …(i)
But mean of 5 numbers = 8
∴ Sum = 8 × 5 = 40 …(ii)
From (i) and (ii)
27 + x + y = 40
⇒ x + y = 40 – 27 = 13
∴ y = 13 – x
(b) Mean of 9 variates = 11
∴ Total sum =11 × 9 = 99
But sum of 8 of these varies
= 7 + 12 + 9 + 14 + 21 + 3 + 8 + 15 = 89
∴ 9th variate = 99 – 89 = 10
(a) The mean age of 33 students of a class is 13 years. If one girl leaves the class, the mean becomes 
years. What is the age of the girl?
(b) In a class test, the mean of marks scored by a class of 40 students was calculated as 18.2. Later on, it was detected that marks of one student was wrongly copied as 21 instead of 29. Find the correct mean.
Solution:
(a) Mean age of 33 students = 13 years
Total age = 13 × 33 = 429 years
After leaving one girl, the mean of 32
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