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The mean of marks scored by $100$ students were found to be $40$ . Later on, it was discovered that a score of $53$ was misread as $83$ . Find the correct mean.

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39.7

53

83

38

answer is A.

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Detailed Solution

It is given that the mean of marks scored by

100

students were found to be

40

. Later on, it was discovered that a score of

53

was misread as

83

.
We need to find the correct mean.
We know that,

Mean = \frac{Sum of observations}{Number o f observations}

\Rightarrow 40 = \frac{x_{1} + x_{2} + x_{3} + . . . . . . . . . . . + x_{100}}{100}

\Rightarrow x_{1} + x_{2} + x_{3} + . . . . . . . . . . . + x_{100} = 40 \times 100

\Rightarrow x_{1} + x_{2} + x_{3} + . . . . . . . . . . . + x_{100} = 4000

According to the given data, one of the score

53

was misread as

83

\Rightarrow Difference in sum = 83 - 53

\Rightarrow Difference in sum = 30

Therefore,

Corrected sum = (x_{1} + x_{2} + x_{3} + . . . . . . . . . . . + x_{100}) - (Difference in sum)

\Rightarrow Corrected sum = (4000) - (30)

\Rightarrow Corrected sum = 3970

Therefore,

New mean = \frac{Corrected sum}{Number of observations}

\Rightarrow New mean = \frac{3970}{100}

\Rightarrow New mean = 39.7

Thus, the correct mean of the data is

39.7

.
Hence, the correct option is 1.

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