Shown below are five cards which are arranged in order from smallest to largest 5 The range of the cards is 4. The median of the cards is 8. The mean of the cards is 7. Work out the 4 missing numbers.

Answer:

5, 5. 8, 8, 9

Explanation:

The five cards are:

5 _ _ _ _

[tex]Range = 4[/tex]

[tex]Median = 8[/tex]

[tex]Mean = 7[/tex]

Required

Complete the numbers

First, we have:

[tex]Range = 4[/tex]

This is calculated as:

[tex]Range = Highest - Lowest[/tex]

So, we have:

[tex]4= Highest - 5[/tex]

Solve for Highest

[tex]Highest = 4 +5[/tex]

[tex]Highest = 9[/tex]

So, we have: 5 _ _ _ 9

Next: [tex]Median = 8[/tex]

This implies that the middle number is 8

So, we have: 5 _ 8 _ 9

[tex]Mean = 7[/tex]

Mean is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

Let the two missing numbers be a and b.

So, we have:

[tex]Mean = \frac{5 + a + 8 + b + 9}{5}[/tex]

[tex]\frac{5 + a + 8 + b + 9}{5} = 7[/tex]

Multiply both sides by 5

[tex]5 + a + 8 + b + 9 = 35[/tex]

Collect like terms

[tex]a + b = 35 - 5 - 8 - 9[/tex]

[tex]a + b = 13[/tex]

Since the number are ordered in ascending order.

And we have: 5 _ 8 _ 9

Then: [tex]5 \le a \le 8[/tex] and [tex]8 \le b \le 9[/tex]

a must be between 5 and 8 (inclusive)

b must be between 8 and 9 (inclusive)

Using trial by error:

[tex]a = 5\ and\ b = 8[/tex]

Because:

[tex]a + b = 13[/tex]

[tex]5 + 8 = 13[/tex]

Hence, the complete list is: 5, 5. 8, 8, 9

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Name:
Date:
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