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Mean of 50 observations was found to be 70.4. But later on, it was discovered that 65 was misread as 56 at one place. Find the correct mean.

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65.28

70.58

75.45

80.93

answer is B.

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Detailed Solution

It is given that the mean of 50 observations is 70.4.
And 65 was misread as 56 at one place.
We have to find the correct mean.
Mean of the data is given by,
Mean =

\frac{x_{1} + x_{2} + . . . + x_{n}}{n}

\frac{x_{1} + x_{2} + . . . + x_{50}}{50} = 70.4

Substituting the known values within the formula and on simplification, we get,

x_{1} + x_{2} + . . . + 65 = 70.4 \times 50

x 1 + x 2 + .... + x 49 + 65 = 3520 x 1 + x 2 + .... + x 49 = 3520 − 65 = 3455

Similarly, when the number 65 was replaced by 56, we get,

x 1 + x 2 + .... + x 49 + 56 = 3520 x 1 + x 2 + .... + x 49 = 3520 − 56 = 3464

The difference between the numbers is given by,

3464 − 3455 = 9

The new mean is given by,

3520 + 9 50 = 352950 = 70.58

The new mean is 70.58
Hence, option 2 is correct.

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