Question

The AM of 50 observations was 100. At the time of calculations, one value was wrongly taken as 100 instead of 180. Find the correct mean​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

The AM of 50 observations was 100.

It means,

Number of observations, n = 50

Mean = 100

We know,

$\boxed{\rm{  \:Mean = \frac{Sum \: of \: observations}{Number \: of \: observations} \: \: }}$

So, we have, according to statement

Incorrect Mean = 100

Number of observations = 50

$\rm \: Incorrect \:Mean = \frac{Incorrect \: Sum \: of \: observations}{Number \: of \: observations} \: \:$

$\rm \: 100 = \dfrac{Incorrect \: Sum \: of \: observations}{50}$

$\rm\implies \:Incorrect \: Sum \: of \: observations = 5000$

Now, it is given that, at the time of calculations, one value was wrongly taken as 100 instead of 180.

Incorrect observation = 100

Correct observation = 180

So,

$\rm \: Correct \: Sum \: of \: observations$

$\rm \: =  \:Incorrect \: Sum \: of \: observations - Incorrect\: observations + Correct \: observations$

$\rm \: =  \:5000 - 100 + 180$

$\rm \: =  \:5080$

$\rm\implies \:\rm \: Correct \: Sum \: of \: observations = 5080$

Now,

$\rm \: Correct \:Mean = \dfrac{Correct \: Sum \: of \: observations}{Number \: of \: observations} \: \:$

$\rm \: Correct \:Mean = \dfrac{5080}{50} \: \:$

$\rm\implies \:\rm \: Correct \:Mean = 101.6 \: \:$

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Additional Information :-

1. If each observation is increased by any constant real number k, mean is also increased by k.

2. If each observation is decreased by any constant real number k, mean is also decreased by k.

3. If each observation is multiplied by any non zero constant real number k, mean is also increased by k.

4. The sum of deviations taken from mean is 0.

Answer 2

CONCEPT:-

Here the above question is based on the concept of data handling We're provided withAM of 50 observations as 100 First of all, we'll calculate data handling and then with the help of that we will find the correct mean It's mentioned in the question thatone value was wrongly taken as 100 instead of 180. so we'll we have to find correct mean so we have get the correct mean

LET US DO THE CALCULATION !!

CORRECT QUESTION :

• The AM of 50 observations was 100. At the time of calculations, one value was wrongly taken as 100 instead of 180. Find the correct mean

GIVEN :

• observations = 50

• 50 observations = 100

• value was wrongly taken as 100 instead = 180

TO FIND :

• WHAT IS THE CORRECT MEAN = ?

SOLUTION :

Average = sum of all observations / No of observations

the mean of 50 observations is 100

100 = sum of 50 observations / 50

100 × 50 = sum of 50 observations

5,000 = sum of 50 observations

one value was wrongly taken as 100 instead of 180

new sum = 5,000 - 100 + 180 = 5,080

new mean = 5,080/ 50

new mean = 101.6

Hence The correct mean is 101.6

ADDITIONAL INFORMATION :

Q 1. WHAT IS DATA HANDLING

• Data handling is the process of ensuring that research data is stored, archiving or disposed off in a safe and secure manner during and after the conclusion of a research project. Proper planning for data handling can also result in efficient and economical storage,retrieval, and disposal of data

Q2 WHAT IS MEAN

The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. Summing the numbers in a set and dividing by the total number gives you the arithmetic mean.