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

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Solution

$M e a n = \frac{S u m o f o b s e r v a t i o n s}{Number of observation}$
$38 = \frac{S u m o f o b s e r v a t i o n s}{9}$
$38 \times 9 = S u m$
$342 = S u m$
As $27$ is mistaken for $72$ , the correct sum of $38$ observations will be,
$342 - 72 + 27 = 297$
The actual mean will be,
$M e a n = \frac{297}{9}$ $= 33$

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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

Mean=SumofobservationsNumber of observation38=Sumofobservations938×9=Sum342=SumAs 27 is mistaken for 72, the correct sum of 38 observations will be,342−72+27=297The actual mean will be,Mean=2979=33

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