Question

the mean of 30 observations is 18.What will be the mean of each observation is increased by 2

Answer 1

Obsevations is 30mean 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←