Arithmetic mean of nine observations is calculated as 38. But in doing

1.	Arithmetic mean of nine observations is calculated as 38. But in doing so, an observation 27 is mistaken for 72. Find the actual mean of the data.
Answer» The mean of 9 observations = 38 The sum of 9 observations = 38 × 9 = 342 If the observation 27 is mistaken for 72 then correct observation = 72 – 27 = 45 Sum of correct observations = 342 + 45 = 387 ∴ Correct Mean = 387/9 = 43

Arithmetic mean of nine observations is calculated as 38. But in doing so, an observation 27 is mistaken for 72. Find the actual mean of the data.

Answer»

The mean of 9 observations = 38

The sum of 9 observations = 38 × 9 = 342

If the observation 27 is mistaken for 72

then correct observation = 72 – 27 = 45

Sum of correct observations = 342 + 45 = 387

∴ Correct Mean = 387/9 = 43