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Mathematics

The mean of n observations is M. If one of these observations is misread as 60 instead of 50, the correct mean is:

  1. M - 50 + 60

  2. M × n - 60 + 50

  3. M×n−60+50n\dfrac{M \times n - 60 + 50}{n}

  4. M×n−50+60n\dfrac{M \times n - 50 + 60}{n}

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Answer

Given,

Mean of n observations is M.

∴ Total sumn=M\dfrac{\text{Total sum}}{n} = M

Total sum = M × n

Given,

One of these observations is misread as 60 instead of 50.

New total sum = M × n - 60 + 50

New mean = New total sumn=M×n−60+50n\dfrac{\text{New total sum}}{n} = \dfrac{M \times n - 60 + 50}{n}

Hence, Option 3 is the correct option.

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