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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Helping Friends
Name:
Date:
Directions: For this assignment you will outline the stages of change and simultaneously explain how
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questions.
1. What is your friend's name? (a fictitious name can be used) (1 point)
2. What is the action or behavior that needs to be changed? (2 points)
3. Complete the chart. (2 points each)
Stage
What actions or characteristics is
your
friend exhibiting that show he/she is
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Pre-

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