Question

MEAN OF 36 OBSERVATION IS 12 . ONE OBSERVATION 47 WAS MISREAD AS 74. FIND THE CORRECT MEAN?

Answer 1

Mean of 36 observations = 12
       Sum of 36 observations = 36 * 12 = 432
 Now, actual Sum = Sum of 36 observations + correct observation - incorrect observation
                                          = 432 +47 - 74 = 405
Hence correct mean = Actual sum of 36 observations / 36
                                          405 / 36
                                              = 11.25

Answer 2

Given:

Mean of 36 observations=12

To find:

The correct mean

Solution:

The correct mean is 11.25.

We can find the mean by following the given steps-

We know that the mean can be calculated by dividing the sum of all observations by the number of observations.

We are given that the number of observations is 36.

The mean of these observations=12

So, the mean=Sum of all observations/ Total number of observations

12=Sum of all observations/36

12×36=Sum of all observations

Sum of all observations=432

Now, we know that one observation was misread.

The wrong observation=74

The correct observation=47

So, the number of observations remains the same.

We will subtract the wrong observation and add the correct observation to the sum of all observations to find the new mean.

The new sum of observations=Sum of all observations-wrong observation+correct observation

=432-74+47

=405

The new mean=new sum of observations/ number of observations

=405/36

=11.25

Therefore, the correct mean is 11.25.