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What would be the correct mean, if the mean of the marks scored by 50 students was found to be 39, further which, it was discovered that a score of 43 was misread as 23?

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49.4

39.4

59.4

69.4

answer is B.

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Detailed Solution

We have to find the correct mean, if the mean of the marks scored by 50 students was found to be 39, further which, it was discovered that a score of 43 was misread as 23.
We know that,

mean = sum of all observations Number of observations

Let the marks scored by the 50 students be

x 1, x 2, x 3, …, x 50

We have been given the mean as 39.
Therefore we have,

39 = x 1 + x 2 + ⋯ + x 50 50 x 1 + x 2 + ⋯ + x 50 = 50 × 39 x 1 + x 2 + ⋯ + x 50 = 1950

Now, the correct mean is,

x 1 + x 2 + ⋯ + x 50 − 23 + 43 50 = 1950 − 23 + 43 50 = 1950 + 20 50 = 197050 = 39.4

So, the correct mean is 39.4.
Therefore, option 2 is correct.

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