Question

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 1

Answer:

5, 5. 8, 8, 9

Explanation:

The five cards are:

5 _ _ _ _

$Range = 4$

$Median = 8$

$Mean = 7$

Required

Complete the numbers

First, we have:

$Range = 4$

This is calculated as:

$Range = Highest - Lowest$

So, we have:

$4= Highest - 5$

Solve for Highest

$Highest = 4 +5$

$Highest = 9$

So, we have: 5 _ _ _ 9

Next: $Median = 8$

This implies that the middle number is 8

So, we have: 5 _ 8 _ 9

$Mean = 7$

Mean is calculated as:

$Mean = \frac{\sum x}{n}$

Let the two missing numbers be a and b.

So, we have:

$Mean = \frac{5 + a + 8 + b + 9}{5}$

$\frac{5 + a + 8 + b + 9}{5} = 7$

Multiply both sides by 5

$5 + a + 8 + b + 9 = 35$

Collect like terms

$a + b = 35 - 5 - 8 - 9$

$a + b = 13$

Since the number are ordered in ascending order.

And we have: 5 _ 8 _ 9

Then: $5 \le a \le 8$ and $8 \le b \le 9$

a must be between 5 and 8 (inclusive)

b must be between 8 and 9 (inclusive)

Using trial by error:

$a = 5\ and\ b = 8$

Because:

$a + b = 13$

$5 + 8 = 13$

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