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The mean of 5 observations is 50. One of the observations was removed from the data, hence the mean became 45. Find the observation which was removed.

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Mean = The sum of all observations/Total number of observations

∴ The sum of all observations = Mean x 

Total number of observations 

The mean of 5 observations is 50 

Sum of 5 observations = 50 x 5 = 250 …(i) 

One observation was removed and mean of remaining data is 45. 

Total number of observations after removing one observation = 5 – 1 = 4 

Now, mean of 4 observations is 45. 

∴ Sum of 4 observations = 45 x 4 = 180 …(ii) 

∴ Observation which was removed = Sum of 5 observations – Sum of 4 observations 

= 250 – 180 … [From (i) and (ii)] = 70 

∴ The observation which was removed is 70.

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