Question

The mean of 20 observation was 40.itwas found later that an observation 53 was wrongly taken as 83.the corrected new mean is

Answer 1

Answer:

38.50

Step-by-step explanation:

mean = ( sum of all observations ) / ( total number of observations )

given:

     total number of observations = 20

     mean of 20 observations = 40

=> ( sum of observations ) / ( 20 ) = 40

=> sum of observations = 40 x 20 = 800

but instead of term 53 the term 83 was  wrongly taken

so the term 83 is removed and new term 53 is added instead of 83.

so subtract 83 from sum of observations and add 53

=> new sum of observations = 800 - 83 + 53

=  770

number of observations does not change, it remains 20

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

= 770 / 20

= 38.50

therefore new mean is 38.50

Answer 2

Answer:

38.5

Step-by-step explanation:

Mean of the observations = 40

Number of observations = 20 observations

Wrongly taken observation = 83

Correct observation in place of wrong observation = 53

$Mean=\frac{Sum\ of\ observations}{Number\ of\ observations}$

Let the sum of observations be X

$40=\frac{x}{20}$

By cross multiplying, we get:

$x=40\times 20$

X = 800 (sum of all observations)

The sum of all observations is 800

As 53 was wrongly taken as 83, 83 must be subtracted from the sum and 53 must be added:

Correct Sum of observations = (800-83)+53

Correct sum of observations = 717 + 53

Correct sum of observations = 770

Now the new sum of observations = 770

No. of observations will remain 20 itself, so the mean  will be:

New mean = $\frac{New\ sum\ of\ obervations}{Number of observations(20)}$

New mean = $\frac{770}{20}$

New mean = $\frac{77}{2}$

New mean = 38.5

The new mean after taking the correct values is equal to 38.5