The mean of 100 observations was found to be 50. If two observations were wrongly taken as 70 and 80 instead of 50 and 60, find the correct mean.

50.6

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49.6

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46.6

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Solution

The correct option is C 49.6
Mean of 100 observations = 50
Since mean = $\frac{s u m o f o b s e r v a t i o n s}{t o t a l n o . o f o b s e r v a t i o n s}$ .
So, sum of observations = $50 \times 100 = 5000$
Now, in the sum, we must subtract the wrong observations and add the correct observations.
So, correct sum of observations
= 5000 - 70 - 80 + 50 + 60
= 4960

Hence, correct mean
= $\frac{c o r r e c t s u m o f o b s e r v a t i o n s}{t o t a l n o . o f o b s e r v a t i o n s}$ .
= $\frac{4960}{100}$ .
= 49.6

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