Answer:
[tex]x = 7[/tex] and [tex]y = 8[/tex]
Step-by-step explanation:
Given
4 6 x y 10
Median = Mean
Required
Find x and y
The mean is calculated as:
[tex]Mean=\frac{4 + 6 + x + y + 10}{5}[/tex]
Collect Like Terms
[tex]Mean=\frac{4 + 6 + 10+ x + y }{5}[/tex]
[tex]Mean=\frac{20+ x + y }{5}[/tex]
The median which is the mid-data is x
i.e.
[tex]Median = x[/tex]
Median = Mean; so, we have:
[tex]x=\frac{20+ x + y }{5}[/tex]
Multiply through by 5
[tex]5 * x=\frac{20+ x + y }{5} * 5[/tex]
[tex]5 x=20+ x + y[/tex]
Collect Like Terms
[tex]5 x - x=20+ y[/tex]
[tex]4x=20+ y[/tex]
Since the numbers are in order, the values of x and y could be any of 7, 8 and 9
Such that:
[tex]x < y[/tex]
So, we need to test the equation with these values
Let x = 7
So, we have:
[tex]4x=20+ y[/tex]
[tex]4 * 7 = 20 + y[/tex]
[tex]28 = 20 + y[/tex]
[tex]28 - 20 = y[/tex]
[tex]8 = y[/tex]
[tex]y = 8[/tex]
This is true for the equation.
Hence:
[tex]x = 7[/tex] and [tex]y = 8[/tex]
