Question

mean of 100 observations Is found to be 40 . if at the time of computation, two items are wrongly taken as 30 and 27 instead of 3 and 72 .find correct mean. ​

Answer 1

Answer:

If mean of 100 observations is found to be 40 but at the time of computation, two items were wrongly taken as 30 and 27 instead of 3 and 72, then the correct mean is 41.8

Step-by-step explanation:

Given mean of 100 observations is 40

That is , 40 = sum of all observations/ 100

Let X be sum of all observations

Then , $\frac{X}{100} = 40\\\\X= 100*40\\\\X=400$

Therefore the sum of all observations is 400

Given that two items were wrongly taken as 30 and 27 instead of 3 and 72.

Therefore, 30+27 and sum of other 98 observations is 400

The real sum of observations is 3 + 72 and sum of other 98 observations.

30+27= 57

3+72 = 75

Therefore change in old sum of observations and new sum of observations = 75-57 =18

So 18 should be added to the old sum of all observations to make it correct

The correct sum of observations = 400+18=418

So the correct mean = sum of all observations/ total number of observations

= 418 /100

=41.8

Answer 2

Correct mean is 40.18 if mean of 100 observations Is found to be 40 and two items are wrongly taken as 30 and 27 instead of 3 and 72

Given:

• mean of 100 observations found to be 40
• Two items are wrongly taken as 30 and 27 instead of 3 and 72

To Find:

• Correct Mean

Solution:

$\text{Mean}=\dfrac{\text{sum of all the obervations}}{\text{number of the observations}}$

Step 1:

Find Sum of 100 observation found.

$40=\dfrac{\text{sum of all the obervations}}{100}\\\\\\\text{sum of all the obervations} = 40 \times 100 = 4000$

Step 2:

Find Correct sum  by subtracting wrongly taken values and adding correct values.

4000 - 30 - 27 + 3 + 72  = 4018

Step 3:

Find Correct Mean

Correct Mean  = 4018/100 = 40.18

Correct mean is 40.18

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