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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.

Respuesta :

mhanifa

Answer:

  • x = 7, y = 8

Step-by-step 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
  • 4,6,x,y,10

Mean:-

[tex]\\ \sf\longmapsto \dfrac{4+6+x+y+10}{5}[/tex]

[tex]\\ \sf\longmapsto \dfrac{x+y+20}{5}[/tex]

Median:-

  • n=5
  • M(D)=n+1/2=5+1/2=3rd term

[tex]\\ \sf\longmapsto M(D)=x[/tex]

Compare

[tex]\\ \sf\longmapsto \dfrac{x+y+20}{5}=x[/tex]

[tex]\\ \sf\longmapsto x+y+20=5x[/tex]

[tex]\\ \sf\longmapsto 4x=y+20[/tex]

[tex]\\ \sf\longmapsto x=y/4+5[/tex]

[tex]\\ \sf\longmapsto x[/tex]

Take pair of (7,8)

[tex]\\ \sf\longmapsto 7=8/4+5\implies 7=2+5[/tex]

Verified

Hence

  • x=7
  • y=8

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