Question

The mean of the data set(9,5,y,2,x) is twice the data set(8,x,4,1,3).what is (y-x)
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Answer 1

`y-x = 16`

Explanation:

Given

Set 1: (9,5,y,2,x)

Set 2: (8,x,4,1,3)

Required

(y - x)

First the mean values of set 1 and set 2 has to be calculated

For set 1

`Mean _1 = ((9+5+y+2+x))/(5)`

Collect like terms

`Mean _1 = (9+5+2+y+x)/(5)`

`Mean _1 = (16+ y+x)/(5)`

For set 2

`Mean _2 = ((8+x+4+1+3))/(5)`

Collect like terms

`Mean _2 = (8+4+1+3+x)/(5)`

`Mean _2= (16+ x)/(5)`

Given that the mean of set 1 is twice the mean of set 2;

`Mean_1 = 2Mean_2`

`(16+ y+x)/(5) =2 * (16+x)/(5)`

Multiply both sided by 5

`5 * (16+ y+x)/(5) = 5 * 2 * (16+x)/(5)`

`16+ y+x = 2 * (16+x)`

Open bracket

`16+ y+x = 32 + 2x`

Subtract 16 from both sides

`16+ y+x- 16 = 32 + 2x - 16`

`16 - 16 + y+x = 32 - 16 + 2x`

`y+x = 16 + 2x`

Subtract 2x from both sides

`y+x-2x = 16 + 2x-2x`

`y-x = 16`