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Q.

The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is 110 not 100. The true mean and median are

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a

50.10,52

b

50,52

c

50.20,52

d

None of these

answer is A.

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Detailed Solution

Given that, mean is 50 and median is 52 for 100 items.
Value of largest item is 100.
Mean can be calculated using the formula,

x ¯ = ∑ x i n

.
Here,

x i

are the individual values, n is number of terms.
Now,

n = 100

and

x ¯ = 50

.

⇒ x ¯ = ∑ x i n ⇒ 50 = ∑ x i 100 ⇒ ∑ x i = 5000

Therefore, true mean is,

x ¯ ′ = ∑ x i n ⇒ x ¯ ′ = 5000 + 110 − 100 100 ⇒ x ¯ ′ = 5010100 ⇒ x ¯ ′ = 50.10

As extreme values do not affect the median, it remains the same.
Thus, the true mean and median are 50.10 and 52.
Therefore, option (1) is correct.

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The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is 110 not 100. The true mean and median are