Question

The mean or 20 observations was 60. It was detected on rechecking that the value of 125
wrongly copied as 25 for computation of mean Find the correct mean.​

Answer 1

Answer:

Correct mean is 65.

Step-by-step explanation:

Given,

Mean of 20 observations was 60.

From the properties of mean :

• Mean = ( sum of observations ) / ( number of observations )

Here,

Mean : 60

Number of observations : 20

= > 60 = ( sum of observations ) / 20

= > 60 x 20 = sum of observations

= > 1200 = sum of observations

The above given sum of observations has a wrong observation, that is 25, that should be 125.

We have to put the correct observation instead of the wrong one.

= > Correct sum of observations = incorrect sum of observations - 25 + 125

= > Correct sum of observations = 1200 - 25 + 125

= > Correct sum of observations = 1300

Then,

Sum of observations : 1300

Number of observations : 20 ( no change, since we subtracted one term and added an other in place of that

Thus,

= > Correct mean = 1300 / 20

= > Correct mean = 130 / 2 = 65

Hence the correct mean is 65.

Answer 2

Let correct mean be M.

• Total number of observations = 20

• Incorrect reading = 25

• Correct reading = 125

Mean = $\dfrac{Sum\:of\: observations}{Total\: number\:of\: observations}$

» Incorrect mean = $\dfrac{Incorrect\:sum\:of\: observations}{Total\: number\:of\: observations}$

=> Incorrect sum of observations = incorrect mean × 60

=> 60 × 20

=> 1200

_____________________________

Correct mean = Incorrect sum of 20 observations - incorrect reading + correct reading

=> 1200 - 25 + 125

=> 1200 + 100

=> 1300

____________________________

Correct mean = $\dfrac{Sum\:of\: observations}{Total\: number\:of\: observations}$

=> $\dfrac{1300}{20}$

=> 65

_____________________________

$\textbf{Correct mean is 65}$

_________ [ANSWER]

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