The mean of $10$ observations was $20$, but later it was found that one observation $25$ was misread as $52$…

The mean of $10$ observations was $20$, but later it was found that one observation $25$ was misread as $52$. What is the correct mean?
  1. $15.7$
  2. $16.5$
  3. $17.3$
  4. $18.0$

Solution

Wrong sum $= 10\times 20 = 200$. Correct sum $= 200-52+25 = 173$. Correct mean $= \dfrac{173}{10} = 17.3$.

Asked in: IMO

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