Question

Here are two sets of numbers, a and b. Set a :200,104,100,160. Set b: 270,400,483,300, x. Mean of set a: mean of set b= 3:8. Work out the value of x

Answer 1

Given:

The given sets are:

Set a : 200, 104, 100, 160.

Set b: 270, 400, 483, 300, x.

Mean of set a: mean of set b= 3:8

To find:

The value of x.

Solution:

Formula for mean:

`Mean=\frac{\text{Sum of observations}}{\text{Number of observation}}`

The mean of set of a is:

`Mean=(200+104+100+160)/(4)`

`Mean=(564)/(4)`

`Mean=141`

The mean of set of b is:

`Mean=(270+400+483+300+x)/(5)`

`Mean=(1453+x)/(5)`

`Mean=(1453+x)/(5)`

It is given that,

Mean of set a: mean of set b= 3:8

`(141)/((1453+x)/(5))=(3)/(8)`

`(705)/(1453+x)=(3)/(8)`

`8* 705=3* (1453+x)`

`5640=4359 +3x`

Isolate the variable x.

`5640-4359 =3x`

`1281 =3x`

Divide both sides by 3.

`(1281)/(3) =x`

`427 =x`

Therefore, the value of x is 427.