five whole numbers are written in order (4, 7, x, y, 11). The mean and median of the five numbers are the same. Work out the values of x and y.

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rjayswaby1977 rjayswaby1977

13-08-2022
Mathematics

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five whole numbers are written in order (4, 7, x, y, 11). The mean and median of the five numbers are the same. Work out the values of x and y.

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MrRoyal MrRoyal · Answer 1 · 2022-08-16T18:38:28+02:00

The values of x and y are 8 and 10, respectively

How to determine the values of x and y?

The list of the numbers is given as:

4, 7, x, y, 11

The mean and median of the five numbers are the same.

The median is the middle number.

So, we have

Median = x

This means that

Mean = Median = x

The mean is calculated as:

Mean = Sum/Count

This gives

(4+ 7+ x+ y+ 11)/5 = x

Evaluate the sum

(22 + x + y)/5 = x

This gives

22 + x + y = 5x

Evaluate the like terms

4x = 22 + y

Based on the order of the list, we have:

7 < x < y < 11

Assume y = 10

4x = 22 + 10

This gives

x = 32/4

x = 8

Recall that:

7 < x < y < 11

This means that

7 < 8 < 10 < 11

The above is true

Hence, the values of x and y are 8 and 10, respectively