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Mathematics

The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

Statistics

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Answer

Given:

Number of observations = 200

Mean = 50

Mean = Sum of all observations Number of all observations \dfrac{\text{Sum of all observations }}{\text{Number of all observations }}

⇒ 50 = Sum of all observations 200\dfrac{\text{Sum of all observations }}{200}

⇒ Sum of all observations = 50 x 200

⇒ Sum of all observations = 10,000

Correct sum of observations = Incorrect sum - incorrect observations + correct observations

= 10,000 - (92 + 8) + (192 + 88)

= 10,000 - 100 + 280

= 10,180

Correct Mean = 10,180200\dfrac{10,180}{200}

= 50.9

Hence, the correct mean is 50.9.

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