Question

the mean of 5 observations is 20 including one new observation the mean is 25 find the newly included observation

Answer 1

Here is the answer
mean=sum/no of observations
20=s/5
s=100
An observation is included so no of observations=6
new mean=(sum of 5 observations +included one) /6
25=(100+x)/6
x=50
so finally the included observation is 50

Answer 2

Given:

The mean of 5 observations=20

New mean=25

To find:

The newly included observation

Solution:

The newly included observation is 50.

We can find the observation by following the given process-

We know that the mean of observations is obtained by dividing the sum of the observations by the total number of observations.

We are given that the mean of 5 obvervations=20

Let the sum of these 5 observations be S.

Mean of observations=S/5

20=S/5

100=S

Now, one observation is added.

So, the new sum of observations=Sum of observations+newly added observation

The new mean=25

The new number of terms=5+1=6

We know that the new mean=New sum of all observations/New number of terms

25=(100+newly added observation)/6

25×6=100+newly added observation

150=100+newly added observation

150-100=newly added observation

Newly added observation=50

Therefore, the newly included observation is 50.