Question

The
mean
of
to observations
is 18 if
each observation is
multiplyied by
2 and
added 3. Then
What is the mean.​

Answer 1

Step-by-step explanation:

Given:-

The mean of two observations is 18.

To find:-

If each observation is multiplyied by 2 and added 3. Then What is the mean?

Solution:-

Given observations = 2

Number of observations = 2

Mean = 18

Let the two observations are x1 and x2

Mean = Sum of all observations / Number of all observations

=>(x1+x2)/2 = 18

=>x1+x2 = 18×2

x1+x2 = 36 ---------------(1)

If each observation is multiplied by 2 and added 3 then they becomes 2x1+3 and 2x2+3

Mean = Sum of all observations / Number of all observations

=>Mean = (2x1+3 + 2x2+3)/2

=>Mean = (2x1+2x2+6)/2

=>Mean = 2(x1+x2+3)/2

=>Mean = x1+x2+3

We have from (1) ,x1+x2=36

=>Mean = 36+3

=>Mean = 39

Answer:-

The new mean of the given problem is 39

Used formulae:-

• Mean = Sum of all observations / Number of all observations
• If the mean of a data is N then if each observation is increased by K then the new mean is N+K
• If the mean of a data is N then if each observation is decreased by K then the new mean is N-K
• If the mean of a data is N then if each observation is multiplied by K then the new mean is NK
• if the mean of a data is N then if each observation is divided by K then the new mean is N/K.