Question

the arithmetic mean of 3 numbers is 30 if 1 is added to every observation what would be the mean​

Answer 1

Explanation:

The average of all the 5 numbers is

x

ˉ

=70.

Hence, the sum of all the five numbers is ∑x=350.

Now, if 100 is added as the 6th number then the average becomes,

6

∑x+100

=

6

350+100

=

6

450

=75.

Answer 2

The arithmetic mean if 1 is added to every observation is 31.

Explanation:

Given:

The arithmetic mean of 3 numbers is 30.

1 is added to every observation.

To Find:

The value of the arithmetic mean if 1 is added to every observation.

Formula Used:

If a,b and c are in are in Arithmetic  Progression (A.P.).

The  arithmetic  mean  $b=\frac{a+c}{2}$ .  ------------- formula no.01.

Solution:

Let  a,b and c are in are in Arithmetic  Progression (A.P.).

As given- the arithmetic mean of 3 numbers is 30.

     $b=30$

Applying formula no.01.

     $b=\frac{a+c}{2}$

    $30=\frac{a+c}{2}$

  $a+c=60$  ----------- equation no.01.

s given- 1 is added to every observation.

hen  a+1,b+1 and c+1  will be  in Arithmetic  Progression (A.P.).

Applying formula no.01.

Now, The  arithmetic  mean $(b+1) =\frac{(a+1+c+1)}{2}=\frac{(a+c+1+1)}{2}$

Putting the value of (a+c)  from equation no.01.

      The  arithmetic  mean $(b+1) =\frac{(60+1+1)}{2}$

                                                        $=\frac{62}{2} =31$

Thus,the arithmetic mean if 1 is added to every observation is 31.

PROJECT CODE#SPJ3