Averages Revision

Averages

Mean, Median, Mode and Range

Frequency Distribution

Cumulative Frequency

Box & Whisker Plots

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

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

​

​Mean Average

Learning Objectives

• Calculate cumulative frequencies

• Plot and draw cumulative frequency curves

• Interprete cumulative frequency curves

• Use cumulative frequency to estimate the median​

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:

Multiple Choice

What number represents the lower extreme or minimum? / ¿Qué número representa el extremo inferior o el mínimo?

• 13

• 16

• 23

• 25

Cumulative frequency column

• The cumulative frequency, cf, gives the number of scores equal to or less than that score.

• The number of times a data value occurs is its FREQUENCY.

Fill in the Blanks

What number represents the lower quartile? / ¿Qué número representa el cuartil inferior?

Dropdown

I can find the mean by ​

Select answer

all of the numbers and then​

Select answer

by how many there are.

Multiple Choice

What is the median shown on this graph? / ¿Cuál es la mediana que se muestra en este gráfico?

• 200

• 250

• 500

• 550

Example 1: Score of 10 students

• How many students scored 7 or less?

• How many students scored 8 or less?

• How many students scored 9 or less?

Multiple Choice

What is the upper quartile? / ¿Qué es el cuartil superior?

• 20

• 30

• 70

• 95

Multiple Choice

Find the mean of 10, 10, 10, 10

• 10

• 20

• 40

• 15

Fill in the Blanks

What is the upper extreme?/ ¿Qué es el extremo superior?

Multiple Choice

How many students are there altogether?

• 1

• 3

• 30

Multiple Choice

What is the upper quartile shown in this graph? / ¿Cuál es el cuartil superior que se muestra en este gráfico?

• 18

• 21

• 21.5

• 23

Multiple Choice

Find the mean of 10, 10, 20, 40

• 10

• 20

• 40

• 15

Multiple Select

How are doing?¿como estas?

• 1 - Good/Bien

• 2 - Questions/Preguntas

• 3 - I don't understand/No entiendo

Multiple Choice

How many students scored 20 or less?

• 3

• 7

• 10

Multiple Choice

Find the mean of the numbers below:

4, 9, 7, 10, 5

• 5

• 6

• 7

• 8

Multiple Choice

How many students scored 30 or less?

• 7

• 13

• 23

Multiple Choice

Find the mean of the numbers below:

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

• 5

• 6

• 7

• 8

Multiple Choice

How many students scored between 10 and 30?

• 7

• 13

• 20

Multiple Choice

Calculate the mean.

16, 5, 7, 12

• 9

• 6

• 12

• 10

Multiple Choice

How many students scored greater than 30?

• 13

• 7

• 6

Multiple Choice

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

• 29
• 38
• 50
• 145

Cumulative frequency nonsense

• You cannot have a cumulative frequency for categorical data.

• For instance, when recording the number of different coloured cars in a parking area it would be nonsense to say there were 13 cars which were blue or less.

Multiple Choice

Find the mean of the numbers below:

20, 30, 24, 30

• 26.5

• 27.5

• 27

• 27.5

Cumulative frequency for grouped data

• A cumulative frequency graph shows the total number of pieces of data up to and including a particular value.

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Rules for construction

• Plot the highest value in each class interval along the horizontal axis.

• Plot the cumulative frequency on the vertical axis.

• Join up the points to give a smooth curve.

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

Example 2

This table shows the heights of some sunflowers.

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

Reading a cumulative frequency graph

• Each point plotted shows you the cumulative frequency up to and including that value.

• The increase in cumulative frequency between each point tells you the frequency of that class interval.

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

Data are above a particular value

• For example, how many sunflowers were taller than 190 cm?

• This tells you how many sunflowers  were less than or equal to 190 cm.

• Subtract the cumulative frequency from the total frequency. 30 – 23 = 7

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

How many students are there altogether?

• 80

• 76

• 6

Multiple Choice

What is the median?

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

Multiple Choice

How many students took up to 20 seconds?

• 6

• 26

• 80

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

How many students took up to 40 seconds?

• 6

• 20

• 29

Multiple Choice

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

• 2

• 3

• 5

• 6

Multiple Choice

How many students took between 20 and 40 seconds

• 6

• 20

• 26

Multiple Choice

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

• 4

• 5.5

• 5

• 6

Multiple Choice

How many students took above 1 minute?

• 62

• 18

• 80

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?

Exercise

Go to your google classroom, and do the assignment individually

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