Question

Five whole numbers are written in order.

4 6 х у
10
The mean and median of the five numbers are the same.
Work out the values of x and y.

Answer 1

• 4,6,x,y,10

Mean:-

`\\ \sf\longmapsto (4+6+x+y+10)/(5)`

`\\ \sf\longmapsto (x+y+20)/(5)`

Median:-

• n=5
• M(D)=n+1/2=5+1/2=3rd term

`\\ \sf\longmapsto M(D)=x`

Compare

`\\ \sf\longmapsto (x+y+20)/(5)=x`

`\\ \sf\longmapsto x+y+20=5x`

`\\ \sf\longmapsto 4x=y+20`

`\\ \sf\longmapsto x=y/4+5`

`\\ \sf\longmapsto x`

Take pair of (7,8)

`\\ \sf\longmapsto 7=8/4+5\implies 7=2+5`

Verified

Hence

• x=7
• y=8

Answer 2

• x = 7, y = 8

Explanation:

Given numbers in order:

• 4, 6, x, y, 10

The mean is same as median.

The median is x as middle number. Since x is a whole number, the mean is also a whole number.

x and y can be selected from 7, 8 or 9 (numbers between 6 and 10).

The mean is:

• (4 + 6 + x + y + 10)/5 =
• (20 + x + y)/5 =
• 4 + (x + y)/5

It should be a whole number, so (x + y) should be divisible by 5.

The option is (7 + 8) = 15, and 9 is excluded.

Let's verify:

• Median = x = 7
• Mean = 4 + (7 + 8)/5 = 4 + 3 = 7