Question

the mean of 200 items was 50. later on it was discovered that two items were misread 92 and 8 instead of 192 and 88. find out correct mean.

Answer 1

As the mean of 200 items is 50. So,
Total items= 200*50 = 10000.
Now,
Difference of items due to misread
= (192-92 )+ (88-8) = 100 + 80 = 180.
Then, Add 180 to the total value
i.e. 10000+180 = 10180.
So, Correct mean= 10180/200 = 50.9

Hope you will find it helpful....

Answer 2

Correct mean is 50.9.

Given:

• Mean of 200 items was 50.
• Later on it was discovered that two items were misread 92 and 8 instead of 192 and 88.

To find:

• Find out correct mean.

Solution:

Formula\Concept to be used:

$Mean=\frac{\Sigma x_i}{n}$

where $\Sigma x_i$:Sum of all observations and n; total observation.

Step 1:

Find the sum of all observations.

Mean = 50

n= 200

Sum of all observations=200×50

Sum of all observations=10000

Step 2:

Find correct sum of all observations.

As instead of 192;92 has been written and for 88;8 was placed.

Thus,

Subtract sum of 92 and 8 and add sum of 192 and 88.

Correct sum of all observations $= 10000 - (92 + 8) + (192 + 88)$

or

$= 10000 - 100 +280$

or

$= 10000 + 180$

or

Correct sum of all observations $\bf = 10180$

Step 3:

Find the correct mean.

According to formula of mean.

$Mean = \frac{10180}{200}$

or

Mean=50.9

Thus,

Correct mean is 50.9.

Learn more:

1) Mean of 20 observations is 15.5. Later it was found that 24 was misread as 42. Find the correct mean.

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2) If the mean of 2,5,8,x,5,6,is 6 then find value of x.

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