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What will be the mean of the given numbers, if there are 50 numbers such that each number is subtracted from 50 and the mean of the numbers so obtained is found to be -3.5?

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46.5

49.5

53.5

56.5

answer is A.

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Detailed Solution

We have to find the mean of the given numbers, if there are 50 numbers such that each number is subtracted from 50 and the mean of the numbers so obtained is found to be -3.5.
We know that,

mean = sum of all observations number of observations

.
Given that the new mean of the 50 numbers after subtracting each number from 50 is

− 3.5

.
Let the numbers be

x 1, x 2, x 3, …, x 50

.
So, the new observations after subtracting 50 from each number is,

x 1 − 50, x 2 − 50, … x 50 − 50

Thus, the new mean is,

new mean = x 1 − 50 + x 2 − 50 + ⋯ + x 50 − 50 50 = x 1 + x 2 + ⋯ + x 50 − 50 × 50 50

Put

− 3.5

for new mean in the above equation, therefore we have,
Question Image

So, the mean of the 50 numbers is 46.5.
Therefore, option 1 is correct.

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