Mean of $40$ observations was given as $160$ .It was detected that $125$ was misread as $160$ . Find the correct mean.

158

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169

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159

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161

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Solution

The correct option is C $159$
Formula used:
$A r i t h m e t i c m e a n = \frac{S u m o f g i v e n n u m b e r s}{T o t a l n u m b e r s}$
Sine, number of observations $, n = 40$
Mean $= 160$ (initial wrong mean)
Incorrected sum $= n \times u = 40 \times 160 = 6400$
Now $125$ was read as $165$ , so
Corrected sum $= 6400 - 165 + 125 = 6360$
$∴$ Corrected mean $= \frac{6360}{40} = 159$

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