Averages and Range

Averages

Mean, Median, Mode and Range

Mean average is where all of the numbers are collected together and shared equally.

"Don't be mean, share." - Anonymous

​

​Mean Average

These three people have 2, 3 and 4 tiles (right)

If we collect them and share them equally, everyone ends up with 3 each.

The mean tells us what people would have if it was an equal share.

​

Visually:

Dropdown

I can find the mean by ​

Select answer

all of the numbers and then​

Select answer

by how many there are.

Multiple Choice

Find the mean of 10, 10, 10, 10

• 10

• 20

• 40

• 15

Multiple Choice

Find the mean of 10, 10, 20, 40

• 10

• 20

• 40

• 15

Multiple Choice

Find the mean of the numbers below:

4, 9, 7, 10, 5

• 5

• 6

• 7

• 8

Multiple Choice

Find the mean of the numbers below:

2, 8, 6, 3, 12, 7, 4

• 5

• 6

• 7

• 8

Multiple Choice

Calculate the mean.

16, 5, 7, 12

• 9

• 6

• 12

• 10

Multiple Choice

Find the mean of these numbers:
2, 57, 38, 42, 6

• 29
• 38
• 50
• 145

Multiple Choice

Find the mean of the numbers below:

20, 30, 24, 30

• 26.5

• 27.5

• 27

• 27.5

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The median represents the middle.

To find the middle it first makes sense to put the numbers in order. Then we can count inwards.

​

Median Average

For example to find the person who is the median height we would have to put them in height order.

Then select the middle person.

So in this case the man in the green shirt has the median height.

​

Median

For numbers it is much the same.

2, 1, 4, 3, 5

Would order to:

1, 2, 3, 4, 5

Then working by crossing out each end until we reach the middle we get:

1, 2, 3, 4, 5
1, 2, 3, 4, 5

Median = 3

​

Median

For numbers it is much the same.

2, 1, 4, 3, 5, 6

Would order to:

1, 2, 3, 4, 5, 6

Then working by crossing out each end until we reach the middle we get:

1, 2, 3, 4, 5, 6
1, 2, 3, 4, 5, 6

In this case we add the two middle numbers and divide by 2

Median = (3 + 4)÷2
= 3.5

​

Median

​Occasionally we have some extra working out to do. This happens when we have an even number of numbers...

Multiple Choice

What is the median?

• biggest- smallest
• average
• the middle #
• # that happens the most

Multiple Choice

When finding the median, what do you do if there are two middle numbers?

• Add them together and divide by 2
• Write them both as the answer
• Give up
• Pick one

Multiple Choice

Find the median of 2, 3, 5, 6, 7

• 2

• 3

• 5

• 6

Multiple Choice

Find the median of 2, 3, 5, 6, 7, 8

• 4

• 5.5

• 5

• 6

Fill in the Blanks

Example 1:

Find the median of 12, 34, 8, 16, 25, 3 and 10

Arrange the data in an increasing order.

3, 8, 10, 12, 16, 25, 34

The middle number is 12

What is the median?

Reorder

Reorder the following

• 5

• 6

• 12

• 18

• 40

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

So the median of 5, 6, 12, 18, 40 is?

• 6

• 9

• 12

• 15

Multiple Choice

What is the median of 1, 2, 3, 4?

• 2

• 3

• 2.5

• 5

Multiple Choice

Find the median of these numbers:
4, 2, 7, 4, 3

• 2
• 5
• 7
• 4

This is the most common number.

Sometimes it is easier to reorder the numbers first.

​

​Mode/Modal Average

You can have up to two modes.

If there are no numbers that appear more than the others you must write "no mode"

​Mode/Modal Average

Multiple Choice

The mode is the number ________________________.

• you see most

• you see least

• you don't see

• you see first

Multiple Choice

At Donald's Donuts the number of donut holes in a bag can vary. Help Donald find the MODE.

12,10,10,10,13,12,11,13,10

• 10

• 12

• 10 and 12

• No Mode

Multiple Choice

What is the mode of the following data set?

5, 7, 7, 8, 12 , 12, 5, 6, 13, 12

• 5

• 7

• 12

• no mode

Multiple Choice

What is the mode in this set of numbers:
7, 14, 20, 3, 7, 14, 2, 14, 7

• 7
• 20
• 7 & 14
• none of the above

Multiple Choice

A data set can have more than one mode

• True
• False

Multiple Choice

What is the mode of this data set?

1, 3, 2, 5, 12, 3, 4

• 4

• 3

• 12

• 1

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The range is a measure of consistency, it tells you have much a set of numbers varies.

​

​The Range

Again it often helps to put the numbers in order before finding the biggest and smallest.

​

​The Range

For the following numbers

​1, 2, 3, 4, 5

The range would be calculated by taking the biggest number "5" and subtracting the smallest number "1"

5 - 1 = 4

So the range=4

Multiple Choice

Anna has test scores of 72, 94, 100, 62.
What is the range of her test scores?

• 32
• 72
• 38
• 100

Multiple Choice

Find the range of the data.

63, 71, 65, 66, 87, 53

• 32

• 33

• 34

• 35

Multiple Choice

Find the range of the data.

16, 28, 6, 19, 21, 15, 22, 33, 17

• 18

• 27

• 30

• 12

Multiple Choice

93, 100, 82, 93, 67, 100, 67, 82, 93, 93
What is the range of this data set?

• 26
• 93
• 33
• 82

Multiple Choice

What is the range of time spent on homework

• 46 min.

• 41 min.

• 31 min

• 77 min.

Multiple Choice

What is the range of speeds tested?

• 0.5 mph

• 1.5 mph

• 0.3 mph

• 1.3 mph

Multiple Choice

What is the range of miniature golf scores?

• 44 points

• 29 points

• 33 points

• 39 points

Multiple Choice

What is the range of Susie's Test Scores?

• 40

• 30

• 15

• 25

Match

Match the following

• Range

• Mode

• Mean

• Median

• Total

Biggest take away smallest

Most Common

Equal Share

Middle Value

Add everything

• Biggest take away smallest

• Most Common

• Equal Share

• Middle Value

• Add everything