Question

the mean of 30 observations is18 what will be the new mean if each observation is increased by 2

Answer 1

Obsevations is 30
mean is 18 
So ,mean the average if increased 2 times:

As we know ,that observations be (x₁,x₂,x₃..............,x₃₀)

for sum of 30 observation which has average18  ,use this formula :$\boxed{\mathrm{Mean = \frac{\Sum~x}{no~of~observation} }} \\\\ \mathrm{Sum~of~observation=(mean)(no~of~observation)} \\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~=(18)(30) \\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~=540$ 

So ,when each is increased by 2,then:

Sum of new observations:
Σx₁=(x₁+2)+(x₂+2)+(x₃+2)+(x₄+2)+....(x₃₀+30)
    =((x₁+x₂+x₃...+x₃₀)+2) x 30
    =((18)+2) x 30
    =540+60
   =600

So,the average is:
mean=              Σx₁                      
              no of new observations
         =  600
              30
         =20←

Answer 2

The new mean = 20

Given :

• Mean of 30 observations is 18

• Each observation is increased by 2

To find :

The new mean

Solution :

Step 1 of 3 :

Write down the sum of observations

Here it is given that mean of 30 observations is 18

So sum of 30 observations

= 30 × 18

= 540

Step 2 of 3 :

Find new sum of observations after increasing each observation by 2

Number of observations = 30

Since each observation is increased by 2

So sum of observations will increased by

= 30 × 2

= 60

So new sum of observations after increasing each observation by 2

= 540 + ( 30 × 2 )

= 540 + 60

= 600

Step 3 of 3 :

Find the new mean

Number of observations = 30

Hence the required new mean

$\displaystyle \sf{ = \frac{New \: sum \: of \: the \: observations}{Number \: of \: observations} }$

$\displaystyle \sf{ = \frac{600}{30} }$

$\displaystyle \sf{ = 20 }$

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