Question

QUESTION
The mean of 100 observations is 50. If one of the observation which was 50 is replaced by 150 then what will be the resulting mean?

Answer 1

Step-by-step explanation:

ANSWER:-

It is given that mean of 100 observations is 50.

So, it will be something like this:-

$\rm{\dfrac{x_1 +x_2 ...}{100} = 50}$

So, what we need to do is, find the value of resulting mean.

But, here is a glitch.

50 is replaced by 150, so how we can rearrange it back?

We can do it!

$\rm{\dfrac{x_1 +x_2 ...}{100} = 50}$

$\rm{x_1 +x_2 ...= 50 \times 100}$

$\rm{x_1 +x_2 ...= 5000}$

Now, we will add 150 to the 5000, because it is the new mean.

But, what will happen of that 50? It was already included!

Simple, we will subtract it.

5000 +150 = 5150

And, subtracting the already included replaced value,

5150 - 50 = 5100

So, resulting mean is 5100. Hence the answer.

Answer 2

Solution :-

The mean of 100 observations is 50 .

As we know that ,

Mean = Sum of observations / Total observations

Let the sum of observations be x

Put the required values,

50 = x / 100

x = 50 * 100

x = 5000

Thus, The sum of observation is 5000 .

Now, One of the observations which was 50 is replaced by 150

Therefore,

According to the question,

5000 - 50 = 4950

Here, One observation that is 50 is subtracted so total observation is 99 But we have to find the mean of 100 observation and it is also given in the question to replace 50 by 150 .

4950 + 150 = 5100

Thus, The new sum of observations is 5100

Now,

By using the formula of mean

Mean = Sum of observation / Total observations

Mean = 5100/100

Mean = 51

Hence, The resulting mean is 51$.$