Q4 of 33 Page 156

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.

Given, mean,

No of observations, n = 9


We know,


Arithmetic mean of x1, x2, x3, …, xn (n observations) is




⇒ sum of observations = x1 + x2 + …+ x9 = 342


As, 27 is mistaken for 72, therefore, actual sum of observations will increase by (72 - 27) = 45


⇒ Actual sum of observations = 342 + 45 = 387




Hence, new mean is 43.


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