Question

A set of integer is arranged in ascending order (x-5) , (x-4) , (x-3) , (x-1) , (x+2) and (x+7) . Find

a) An expression of its median in terms of x
b) An expression of its mean in terms of x
c) Value of x if its mean is twice its median

Answer 1

The number of terms here are even = 6.
When terms are even, median is the average of two middle terms.
Therefore,

median =
`(x-3+x-1)/(2) = (2x-4)/(2) = x-2`

Mean =
`(x-5+x-4+x-3+x-1+x+2+x+7)/(6) = (6x-4)/(6)`

Mean = 2(median)

`(6x-4)/(6) = 2(x-2)`

`6x-4 = 12(x-2)`

`6x-4 = 12x-24`

`6x=20`
Therefore, x =
`(10)/(3)`