vanelise
contestada

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

Respuesta :

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

median = [tex] \frac{x-3+x-1}{2} = \frac{2x-4}{2} = x-2[/tex]

Mean = [tex] \frac{x-5+x-4+x-3+x-1+x+2+x+7}{6} = \frac{6x-4}{6} [/tex]

Mean = 2(median)
[tex] \frac{6x-4}{6} = 2(x-2)[/tex]
[tex]6x-4 = 12(x-2)[/tex]
[tex]6x-4 = 12x-24[/tex]
[tex]6x=20[/tex]
Therefore, x = [tex] \frac{10}{3} [/tex]

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