Statistics

Lesson

Graphs are a visual way of presenting information. They can be really useful as they help us sort and order the information we collect and present it in a clear, concise way. Selecting a good type of graph to display your data is really important and the best type of graph to pick will change depending on the type of information you need to display. Let's run through a few different types of graphs now.

A picture graph is a statistical graph for organising and displaying **categorical** data (that is data that can be split into different categories or groups). It uses pictures or symbols to represent data. Picture graphs have a **key**, which is like a little instruction box that explains what each symbol means. For example, in the graph below, the key says that one bus represents $40$40 children. Each column of buses represents how many children caught the bus each day. So if you look in the "Monday" column, there are $2$2 buses. This means that $2\times40$2×40, or $80$80 children caught the bus on Monday.

A high school did a student survey on how students travel to school. They recorded this data on a picture graph shown here. Use the key and the graph to answer the questions below.

How many students rode a bike to school?

162

A30

B3

C300

D162

A30

B3

C300

DWhat was the most common form of transport?

Car

ABus

BTrain

CBike

DCar

ABus

BTrain

CBike

DHow many children caught the bus to school?

6

A300

B64

C324

D6

A300

B64

C324

DHow many children arrived by car?

540

A45

B400

C243

D540

A45

B400

C243

DHow many students are there in total in the school?

A table is another great way to display data in an organised way. In a table, the headings of the various things we have measured label the columns. Each row will show all the characteristics about one particular item or person.

Let's look at the table below:

Name | Age | Favourite Animal |
---|---|---|

George | 12 | Tiger |

Yi | 11 | Parrot |

Sarah | 12 | Koala |

If we look at the column headings, we can see we have collected information about three topics: people's names, ages and favourite animals.

We can read across the rows to see all the information that relates to each person. For example, Sarah is $12$12 and her favourite animal is a koala.

Below is a table showing the prices of different cards.

Code | Price |
---|---|

AA | $\$1.30$$1.30 |

BB | $\$1.80$$1.80 |

CC | $\$2.90$$2.90 |

DD | $\$3.20$$3.20 |

EE | $\$3.50$$3.50 |

**a)** Darren has $\$3.70$$3.70 to buy $2$2 birthday cards. Will he have enough to buy a card with code BB and a card with code CC?

**Think:** What would the total of these two cards be? Let's look at the table to find the price of each item.

**Do:** $1.80+2.90=\$470$1.80+2.90=$470

Darren only has $\$3.70$$3.70 so he does not have enough to buy a BB and a CC card.

**b)** Suzie buys a card as well. She pays with a $\$5$$5 note and gets $\$1.80$$1.80change. What is the code on her card?

**Think:** The price Suzie paid is the difference between the amount Suzie paid and the change she received.

**Do:** $5-1.80=\$3.20$5−1.80=$3.20

Let's look at the table to see which card costs $\$3.20$$3.20?

Suzie bought a DD card.

Study this diagram which shows the relationship between children and their favourite pets, then answer the following questions.

What is Mark's favourite pet?

hamster

Akitten

Bpuppy

Cbunny

Dturtle

Ehamster

Akitten

Bpuppy

Cbunny

Dturtle

EWhose favourite pet is a puppy?

James

ASally

BEmily

CSarah

DMark

EJames

ASally

BEmily

CSarah

DMark

EWhat is Sally's favourite pet?

puppy

Aturtle

Bhamster

Cbunny

Dkitten

Epuppy

Aturtle

Bhamster

Cbunny

Dkitten

E

The following Venn diagram illustrates the types of movies children in a class like to watch.

How many children like thriller movies only?

$\editable{}$

How many children like action movies only?

$\editable{}$

How many children like animation movies only?

$\editable{}$

How many children like BOTH animation and action movies?

$\editable{}$

How many children like BOTH thriller and action movies?

$\editable{}$

Study the bar graph below, which shows the changes in tourism rates in different cities during 2011 and 2012 , then answer the following questions.

What is the difference between Shanghai's percentage of tourism over the 2 years?

$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

D$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

DWhich city had the greatest difference in percentages of tourism over 2011 and 2012?

London

ATokyo

BRome

CNew York

DLondon

ATokyo

BRome

CNew York

DWhich city had the smallest difference in minimum and maximum percentages of tourism over 2011 and 2012?

Singapore

AIstanbul

BDubai

CParis

DSingapore

AIstanbul

BDubai

CParis

DWhat is the difference between the minimum and maximum percentages of tourism of all the cities in the graph over the 2 years.

$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D

Graphs are a visual way of presenting information. They can be really useful as they help us sort and order the information we collect and present it in a clear, concise way. Selecting a good type of graph to display your data is really important and the best type of graph to pick will change depending on the type of information you need to display. Let's run through a few different types of graphs now.

A Venn diagram is a great way of displaying multiple sets of categorical data

John Venn created the Venn diagram as a way of picturing relationships between different groups of things. In other words, Venn diagrams are a great way of displaying different sets of categorical data, as we can easily see what is common between the groups and what is different between the groups.

In a Venn diagram, each group is represented by a separate circle. If the circles overlap, this shows a similarity between the two groups. For example, say we wanted to display the different types of sports people like. In the diagram people, the blue circle might represent people who like soccer and the orange circle might represent people who like cricket. The area in the middle where the circles overlap, represents people who like *both* soccer and cricket.

We can even display more than two groups. Check out the three groups shown below. See how we display the similarities and differences between the three groups?

The following Venn diagram illustrates the types of movies children in a class like to watch.

How many children like thriller movies only?

$\editable{}$

How many children like action movies only?

$\editable{}$

How many children like animation movies only?

$\editable{}$

How many children like BOTH animation and action movies?

$\editable{}$

How many children like BOTH thriller and action movies?

$\editable{}$

A divided bar graph is a rectangle (or bar) that is split up into different sections like this:

The size of each section represents the proportion of the "whole" that is being graphed. It is important to know the exact size of the whole, as each section of the bar represents a fraction of that amount. We can see in the graph above that hockey is the least popular sport, as it takes up the smallest part of the bar. Conversely, soccer is the most popular sport as it takes up the biggest amount of the bar.

A high school did a student survey on how students travel to school. They recorded this data on a picture graph shown here. Use the key and the graph to answer the questions below.

How many students rode a bike to school?

162

A30

B3

C300

D162

A30

B3

C300

DWhat was the most common form of transport?

Car

ABus

BTrain

CBike

DCar

ABus

BTrain

CBike

DHow many children caught the bus to school?

6

A300

B64

C324

D6

A300

B64

C324

DHow many children arrived by car?

540

A45

B400

C243

D540

A45

B400

C243

DHow many students are there in total in the school?

Study this diagram which shows the relationship between children and their favourite pets, then answer the following questions.

What is Mark's favourite pet?

hamster

Akitten

Bpuppy

Cbunny

Dturtle

Ehamster

Akitten

Bpuppy

Cbunny

Dturtle

EWhose favourite pet is a puppy?

James

ASally

BEmily

CSarah

DMark

EJames

ASally

BEmily

CSarah

DMark

EWhat is Sally's favourite pet?

puppy

Aturtle

Bhamster

Cbunny

Dkitten

Epuppy

Aturtle

Bhamster

Cbunny

Dkitten

E

Study the bar graph below, which shows the changes in tourism rates in different cities during 2011 and 2012 , then answer the following questions.

What is the difference between Shanghai's percentage of tourism over the 2 years?

$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

D$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

DWhich city had the greatest difference in percentages of tourism over 2011 and 2012?

London

ATokyo

BRome

CNew York

DLondon

ATokyo

BRome

CNew York

DWhich city had the smallest difference in minimum and maximum percentages of tourism over 2011 and 2012?

Singapore

AIstanbul

BDubai

CParis

DSingapore

AIstanbul

BDubai

CParis

DWhat is the difference between the minimum and maximum percentages of tourism of all the cities in the graph over the 2 years.

$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D

Graphs are a visual way of presenting information. They can be really useful as they help us sort and order the information we collect and present it in a clear, concise way. Selecting a good type of graph to display your data is really important and the best type of graph to pick will change depending on the type of information you need to display. Let's run through a few different types of graphs now.

Column graphs are used to show categories of data that you have counted. In a column graph, the height of the column shows the number of scores. Both the horizontal and vertical axes should be labelled to help explain the information in the graph. Look at the example below. The horizontal axis tells us the number of laps that were walked and the vertical axis tells us the number of children. For example, six children walked between $26$26 and $30$30 laps.

Look at the column graph above. How many laps did $11$11 children walk?

Think: Look up the vertical axis to $11$11, then move across the graph in a straight line to see which column corresponds to this.

Do: $11$11 children walked between $21$21 and $25$25 laps.

Histograms are similar to bar or column graphs. There are 2 main differences:

- Bar or column graphs are usually used to display "categorical data", whereas histograms are used to display “numerical data”
- Bar and column graphs are drawn with spaces between the columns whereas histograms do not have spaces between the columns.

Histograms can display discrete or continuous numerical data.

For example each student in a class were surveyed and asked the number of children in their family. This histogram shows the results of this survey.

Line graphs are used to display continuous data and are often used to show changing information. Examples of data that could be displayed in a line graph include temperature, your heart rate throughout the day and a company's daily sales.

Basically, a line graph is drawn as one continuous line to show a continual (usually changing) set of scores.

The line graph below shows how the temperature changed throughout the day.

a) What was the temperature at $6$6am?

Think: Let's find $6$6am on the horizontal axis, then look up to the red line, then to the corresponding point on the vertical axis.

Do: It was $15^\circ$15°C at $6$6am.

b) At what time was the temperature the hottest?

Think: When does the red line reach the highest point?

Do: It is hottest at $2$2pm.

c) How much cooler was it at $7:30$7:30am than at $10:30$10:30am?

Think: What were the temperatures at both of these times? What is the difference between them?

Do:

At $10:30$10:30am, it was $25^\circ$25°C. At $7:30$7:30am, it was $20^\circ$20°C.

$25-20=5$25−20=5

It was $5^\circ$5°C cooler at $7:30$7:30.

A high school did a student survey on how students travel to school. They recorded this data on a picture graph shown here. Use the key and the graph to answer the questions below.

How many students rode a bike to school?

162

A30

B3

C300

D162

A30

B3

C300

DWhat was the most common form of transport?

Car

ABus

BTrain

CBike

DCar

ABus

BTrain

CBike

DHow many children caught the bus to school?

6

A300

B64

C324

D6

A300

B64

C324

DHow many children arrived by car?

540

A45

B400

C243

D540

A45

B400

C243

DHow many students are there in total in the school?

Study this diagram which shows the relationship between children and their favourite pets, then answer the following questions.

What is Mark's favourite pet?

hamster

Akitten

Bpuppy

Cbunny

Dturtle

Ehamster

Akitten

Bpuppy

Cbunny

Dturtle

EWhose favourite pet is a puppy?

James

ASally

BEmily

CSarah

DMark

EJames

ASally

BEmily

CSarah

DMark

EWhat is Sally's favourite pet?

puppy

Aturtle

Bhamster

Cbunny

Dkitten

Epuppy

Aturtle

Bhamster

Cbunny

Dkitten

E

The following Venn diagram illustrates the types of movies children in a class like to watch.

How many children like thriller movies only?

$\editable{}$

How many children like action movies only?

$\editable{}$

How many children like animation movies only?

$\editable{}$

How many children like BOTH animation and action movies?

$\editable{}$

How many children like BOTH thriller and action movies?

$\editable{}$

Study the bar graph below, which shows the changes in tourism rates in different cities during 2011 and 2012 , then answer the following questions.

What is the difference between Shanghai's percentage of tourism over the 2 years?

$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

D$25%$25%

A$10%$10%

B$20%$20%

C$15%$15%

DWhich city had the greatest difference in percentages of tourism over 2011 and 2012?

London

ATokyo

BRome

CNew York

DLondon

ATokyo

BRome

CNew York

DWhich city had the smallest difference in minimum and maximum percentages of tourism over 2011 and 2012?

Singapore

AIstanbul

BDubai

CParis

DSingapore

AIstanbul

BDubai

CParis

DWhat is the difference between the minimum and maximum percentages of tourism of all the cities in the graph over the 2 years.

$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D$55%$55%

A$65%$65%

B$40%$40%

C$60%$60%

D

Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods;– gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays.