University of Tasmania, Australia

Understanding 1

Data are collected by governments, businesses, service industries (including schools), marketing organisations, communities and individuals. These data are used in many different ways to understand what is happening and to make decisions.

Australian Bureau of Statistics

To collect data, the Australian Bureau of Statistics conducts a Population Census every 5 years. The next Australian census is in August 2016.

View the Population and How It Is Measured video.

View the Spotlight 2.0 app to learn about some of the information gathered by the census.

Download the Run That Town Strategy Game. Use real census data to make decisions about projects in your local area.

The Australian Bureau of Statistics collects many other data sets that include information about the weather, economic and financial trends, traffic flow rates, and data about unemployment rates.

Visit the Australian Bureau of Statistics website and download some of the Product Releases and the Media Releases  to find out more about the data collected and analysed.

Learning Activity 1

Focus: Extracting data from written reports

View the following data set and answer the questions below.

Australian International Visitor Survey Summary

Questions

1. What is the most common reason given as to why international visitors come to Australia?
2. What percentage of visitors came to Australia for employment opportunities?
3. What is the total number of nights stayed by visitors in Australia during the data collection period?

Click here to check your answers 

Learning Activity 2

Focus: Interpreting data in tables

View the following data sets and answer the questions below each link.

Steps taken in the last 12 months to save water-by State

Questions

1. How many households in South Australia use water from a rainwater tank?
2. What proportion of households in the Australian Capital Territory does not water their lawn or garden?
3. Which state has the most number of households that do not report any saving activities?
4. Which state is the best at using water saving strategies?
5. Why are there so few households in the Northern Territory that use water from a rainwater tank?

 
Children participating in selected activities, by Sex, 2006-2012 (3 year
intervals)

 Table Soc5 (towards the bottom of the page)

Questions

1. Name two activities that showed a steady increase in participation rates for males and females for each of the intervals across 2006-2012?
2. The male participation rate for “Reading for pleasure” decreased by 3.7% from 2006-2012. The female participation rate also decreased over that time. Was the decrease in the female participation rate greater or less than the decrease in the male participation rate?  
3. Compare the participation rates for males and females for "Australian Rules" and "Outdoor Cricket". Write two or three sentences that describe the variation in the data across the years for the two sports.  

Life expectancy at birth, by State, 1971 to 1995 and 1993-95 to 2004-06

Table Soc1 (at the top of the page)

To use something other than categorical data – life expectancy at birth (by state) can also be found on the above web site.

Question

Write three questions that could be answered from the data about life expectancy in the table.

Click here to check your answers

Learning Activity 3

Focus: Interpreting data in graphs

An interactive graph looking at unemployment rate

The graph on the web page can be changed by selecting one of the three different options in the drop-down menu beneath the graph. You will need to select the different options to answer the following questions.

Questions

1. What is the lowest unemployment rate during the period 2002-2012 and in which year did it occur?
2. In 2002 the unemployment rate for males was greater than the unemployment rate for females. In which other year was the unemployment rate for males greater than the unemployment rate for females?
3. Write a story that describes the change in the longer term unemployment rates from 1979-2012?

Click here to check your answers

Check Your Understanding of Big Idea 1

The purpose of this Big Idea was for you to describe and find different types of data that are collected by businesses, government, service industries, communities and individuals.

If you have completed the questions and understand how to describe and find different types of data then continue on to Big Idea 2 in the Data and Statistics Module.

Understanding 1

A variable is any measurable characteristic or attribute that can have different values for different subjects. Height, age, amount of income, country of birth, grades obtained at school and type of housing are examples of variables.

View the video (no audio)

What are Variables?   

Visit the Glossary of Statistical Terms to get more explanations about different types of variables and data representations.

Learning Activity 1

Focus: Types of data – categorical and numerical

Classifying different types of data is necessary to know if performing calculations on the data are possible and to know which graphical representation is appropriate for displaying the data.

Categorical data are often represented in bar charts and pie charts.

• Categorical data can be sorted into groups or categories.
• It is not possible to perform calculations on categorical data.

Examples: eye colour, shoe size, gender, month of birth.

Numerical data are counts or measures.

• Numerical data are often represented in line graphs or scatter plots.
• It is possible to perform calculations on numerical data, such as finding the mean height of a group of students.
• Numerical data can be placed in ascending or descending order.

Examples: speed, quantities, age, distance.

Complete the activity.

What’s the Difference Between Numerical and Categorical Data?

At the bottom of the page there are links to download the worksheet and the solutions.

Learning Activity 2

Focus: Displaying different types of data

In this activity you will identify the two different types of data presented in graphs and use the graphs to answer questions about the data.

Graph 1: Cereal manufacturers

This graph shows the number of different breakfast cereal products made by seven different manufacturers. The names of the manufacturers are used as categories to organise the data. 
 

Questions

1. How many different types of cereal are made by Sanitarium?
2. Which manufacturer makes the most different types of cereal?

Chick here to check your answers

Graph 2: Number of cereal boxes on three supermarket shelves

This graph shows the placement of each manufacturer’s breakfast cereal products on three supermarket shelves.

Questions

1. Which shelf has the most breakfast cereal products on it?
2. Which manufacturers only have breakfast cereal products on the middle shelf?
3. What conclusions can be drawn from seeing that Woolworths’ breakfast cereals are only placed on the middle shelf?

Click here to check your answers
 

Graph 3: Sugar content in breakfast cereal products

This graph shows the sugar levels in the breakfast cereals. The data are sorted according to the manufacturer. The amount of sugar for each product is expressed as the number of grams of sugar per 100 grams of breakfast cereal and is sorted into bins.

Questions

1. If you were trying to make a healthy cereal choice, which manufacturer would you choose and why?
2. How many breakfast cereal products have 10 grams or more of sugar per 100 grams of breakfast cereal?
3. What is the sugar level that occurs the most in the breakfast cereal products?

Click here to check your answers

Graph 4: Arrangement of products on the shelves according to sugar content levels

Questions

1. What is the range of the sugar level that has the most breakfast cereal products?
2. What conclusions can be drawn from the graph about the placement of the breakfast cereal products on the shelves?
   

Click here to check your answers

Graph 5: Sugar content in breakfast cereal

This graph shows the distribution of the sugar content in the breakfast cereal products. The distribution shows the variation in the sugar content across the range of sugar content levels for all the products. The range is the lowest to the highest value in the data set.
 

Questions

1. What is the range of the sugar content in the breakfast cereals?
2.  From the graph, estimate the average sugar content of the breakfast cereal products. 
   

Click here to check your answers

Overview Questions

1. Which graphs display categorical data?
2. Which graphs display numerical data?
3. Which graphs display a combination of both categorical and numerical data?

Click here to check your answers

Check you Understanding of Big Idea 2

The purpose of this Big Idea was to;

• Recognise the difference between categorical and numerical data
• Extract data from tables and graphs

Does this make sense to you now?

If so, continue on to Big Idea 3 in the Data and Statistics Module.

Understanding 1

Often, a set of data is made up of many different cases and multiple pieces of information are collected for each case.

For example, a class of students in Grade 5 collected data about their physical characteristics and recorded the information for all the students in the one data set. The physical characteristics for each student were recorded.

In the data set, each student in the class is an individual case and the physical characteristics of the students are attributes. These data may be recorded on data cards, which are used to sort and organise the data

In this data card, the student, Nicholas, has a height of 169.0 cm and a hand span of 19.0 cm. Nicholas' information has been recorded as Case 11 in a data set of 40 students. The attributes are Belly Button Height, Hand Span, Foot Length, Height, and Gender.

Graphs are used to represent the data in data sets. They display data in ways that assist in using the data to answer questions. Different types of graphs are needed to answer different questions and the selection of the type of graph depends on the question being asked and the data available. Data can also be organised and displayed in tables

The Grade 5 data set is a multivariate data set. It has multiple attributes for multiple cases. To answer questions about the data set, it is not always necessary to use all the data at once. Creating a graph with data for one attribute is using univariate data. Creating a graph with data from two or more attributes is using multivariate data.

Example 1: Using Univariate Data

"What is the most common Foot Length of students in Class B?"

To answer the question it is only necessary to use the Foot Length data.

The graph showing the Foot Length for Class B is displaying univariate data. The graph can be used to answer directly the question, "What is the most common Foot Length of students in Class B?"

Example 2: Using Bivariate Data

"Is there a relationship between the Belly Button Height and Height of students in Class B?"

To answer the question it is necessary to use the data from two attributes - Belly Button Height and the Height data.

The graph showing the relationship between Belly Button Height and Height for Class B is displaying multivariate data, or more specifically, bivariate data. The graph can be used to answer directly the question, "Is there a relationship between the Belly Button Height and Height of students in Class B?"

Example 3: Using Multivariate Data

Visit the Weatherzone website to view Hobart's Annual Temperatures and Rainfall data. The graph is an example of how multiple attributes can be displayed in the one graphical representation. The legend under the graph details the different elements displayed in the graph. The data are also displayed in tables. Use the graph or the tables to answer the following questions.

Weatherzone website

Questions

1. What is the mean maximum temperature for Hobart in June?
2. Which month is Hobart likely to get the most rain?
3. What was the temperature in Hobart when it experienced its hottest maximum temperature?
4. What are the average number of days in a year that Hobart experiences temperatures at or below 20 C?
5. Use the search engine on the Weather Zone website to look for weather information for the area you are located in. You can search by town name or postcode.
   

Click here to check your answers

Example 4: Different Graph Types

Many different types of graphs can be used to display data and answer questions about the data.

 View the video below, ABS - CensusAtSchool - Draw a Graph, to learn how to create graphs in Excel.

Learning Activity 1

Focus: Categorising, sorting and representing categorical data

Variety on the Menu

The dishes on the menu at a local restaurant are categorised according to the main ingredient in each dish. The categories are Beef, Fish and Seafood, Chicken, Vegetarian, and Meat and Vegetable Combinations.

Organising data in a table
The total number of dishes in each category on the menu is presented in the table below. The table also displays the number of dishes as a fraction of the total number of dishes on the menu, which is also converted to a decimal and into a percentage.  

Complete the table

Questions

1. How many dishes have vegetables?
2. What percentage of the menu includes vegetables?
3. What fraction of the menu is available for diners who only want to order beef or chicken?
4. Which category of dish contributes to a little over a quarter of dishes on the menu?

Displaying data in a graph

The graph below displays the categories of dishes from the menu together with the quantity and percentage data. Pie charts are good for displaying categorical data when percentages are calculated.

Learning Activity 2

Focus: Comparing data

Graphs can be used to compare data from two or more data sets or compare two or more attributes from the same data set.

Bruny Island Rainfall

Comparing two data sets

The Bureau of Meteorology is Australia's national weather, climate and water agency.

It maintains national climatic records and water information to the Australian community. It has been recording the temperature and rainfall in Hobart for 120 years.

The graph below was constructed using some of that data. It displays the mean rainfall for each month in 1890 and 2013. Representing the rainfall data for the two years on the same graph allows direct comparison to be made.

Questions

1. In general, was 1890 a wetter year than 2013 on Bruny Island? Use details from the graph to justify your answer.
2. Which months of the year support your conclusion?
3. What months of the year contradict your conclusion?

Please note: No inferences about global warming can be made from these data. Much more evidence from multiple sources is required before such claims can be made.

Click here to check your answers

Learning Activity 3

Focus: Comparing data

Does gender make a difference?

Students in a Grade 6 class recorded their heart rate in beats per minute before doing any exercise.

This was their Resting Heart Rate. They then recorded their heart rate after they has run around the school oval. This was their Active Heart Rate.

One of the students graphed the Active Heart Rate data to see if there was a difference between the boys and the girls in the class.

Use the graph to answer the questions below.

Questions

1. What is the range of the data for the boys in the class?
2. Which is the active heart rate for the girls that occurs the most?
3. Compare the boys’ active heart rates with the girls’ active heart rates. What conclusions can be drawn from the data? Use the data in the graphs to justify your conclusions.

Click here to check your answers

Learning Activity 4

Focus: Looking for relationships in data

Scatter Plots

It is also possible to find relationships between different attributes in a data set using scatter plots. In scatter plots each data point is a representation of two values, which must be numerical data values.

Ozone Levels

The U.S. Environmental Protection Agency (EPA) has set a standard of ground level ozone at 120 parts per billion (ppb), meaning that it considers levels higher than this to be unsafe. But research suggests that for people with asthma, long periods of exposure to a level of even 50 ppb can be harmful.

View the video that explores data collected about the ozone levels in New York in 1973.

Questions

1. What effect does temperature and wind speed have on the ozone levels?
   
   

    
2.  
3. What percent of the days in these data had ozone levels that exceeded the EPA limit of 120 ppb?
4. What percent of the days in these data had an ozone level that is potentially dangerous for people with asthma?
   

This activity was developed from a data set from TinkerPlots Data Dynamic Data Exploration

Click here to check your answers

Learning Activity 5

Focus: Looking for relationships in data

Does gender make a difference

Data can be used to see if there is a relationship between children’s height and their belly button height.

The general trend in the graph below shows that the belly button height increases as height increases. The wide spread of the data indicates that it is not a close relationship but the general upward trend of the data in the graph suggests there is a relationship, overall.

The following four graphs have a hand drawn trend line added. It shows an approximation of the relationship between Height and Belly Button Height.

Also added are reference lines that intersect with the trend line. The values of the height and belly button height that apply to the point of intersection are noted on the graph. For example, Graph (i) the point of intersection has a Height value of 157cm and a Belly Button Height of 97cm.

Dividing the height value by the belly button height value will quantify the relationship between height and belly button height as a ratio.

Questions

1. Use the data in the four graphs to complete the following table.
2. Find the average of the four calculations made.
3. Write a sentence describing what you have found about the number of times greater people’s height is to their belly button height.
4. Why is it necessary to take multiple points and then find the average of the four calculations?
    

Graph (i)

Graph (ii)

Graph (iii) 

Graph (iv)

Click here to check your answers 

Understanding 2

Data can be summarised to represent the whole data set

The characteristics of the data can be used to represent the whole data set. These characteristics are referred to as descriptive statistics. Descriptive statistics are used to describe and represent the data set as well as to compare a data set with other data sets.

Measures of central tendency

Measures of central tendency are summary statistics that measures the middle (or centre) of the data. These are known as the mean, median, and mode.

• The mean is the average of all observations in a set of data.
• The median is the middle observation in an ordered set of data.
• The mode is the most frequent observation in a set of data.

View the Statistics Intro: Mean, Median, and Mode from Khan Academy.

View the Example: Finding the Mean, Median, and Mode from Khan Academy

For more information, read Examples of Measures of Central Tendency provided by the Australian Bureau of Statistics.

Example of the mean represented in a graph

The triangle and the blue line identify the mean sugar levels in breakfast cereal products.

All Khan Academy content is available for free at www.khanacademy.org

Learning Activity 6

Mean, median and mode

Calculating the Mean, Median, and the Mode

Complete the following worksheet

 Calculating the Mean, Median, and the Mode Worksheet 

The worksheet was generated from the http://www.math-aids.com/ website.

Using the mean to compare two groups

In this graph the mean active heart rates for boys and girls are denoted by the small blue triangle and the line.

There is approximately a difference of 30 beats per minute between the mean active heart rate for girls and the boys.

Because there is a large difference between the two means, it can be suggested that the boys and girls cannot be considered to be the same when it comes to active heart rate.

Using the mean to compare two groups

In this graph the mean sugar level in each of the manufacturers’ breakfast cereal products is denoted by the small blue triangle. The numerical values of the means are also added to the graph. The manufacturers listed in no particular order.

Questions

1. List the manufactures in order of the mean sugar levels in their breakfast cereal products.
2. Use the mean sugar levels to group the manufactures into two groups. What is the range of the mean sugar levels for the two groups?
3. Find the mean of the mean sugar levels in each group. Do you think the difference in the two new means calculated suggests there is a difference between the two groups of manufactures?

Click here to check your answers

Check your Understanding of Big Idea 3

The purpose of this Big Idea 3 was to demonstrate the following understandings;

• Comparing two related data sets represented in a graph
• Describing the relationship between selected bivariate data
• Describing the general features of a data set including mean, median, mode and range

Please proceed to Big Idea 4 in the Data and Statistics Module

Understanding 1

In many cases, data are collected from large sets. The Population Census collects data from everyone in Australia – in other words the population of Australia. The word population has a special meaning in statistics – it is any complete group of people, animals, plants or things with at least one characteristic in common.

Watch this short video on Populations from the Australian Bureau of Statistics (the video has no audio).

Populations

Question

It is important to clearly define you population in order to:

a. To save time in collecting your data
b. To make sure that the data you collect is useful to you
c. To help you prepare the table for presenting the data
d. All of the above

Click here to check your answer

It is not always possible to collect data about a whole population. This does not mean that we cannot obtain useful data. We can use a sample that can help us predict what we would find if we collected data from the whole population. It is important that we choose this sample wisely – it must be able to provide a representation of the whole population that is reliable.

Samples may be randomly selected or purposefully selected.

A familiar sampling technique is that used by telephone opinion poll companies, such as Newspoll and Roy Morgan Research.

Newspoll is conducted by the Australian newspaper who canvases the general public on issues such as voting preferences at election time, market research for new products, and social issues, such as the standard of living.

If you have been contacted by such companies, you will notice that the caller wants demographic information, such as your age or gender. This would be to ensure that the sample is representative of the population targeted.

The companies want to avoid getting too many responses from one particular age group and not enough responses from other age groups. For other surveys, they may only want to target a particular age group, which would be purposeful sampling.

View the Reasonable Samples video from Khan Academy that considers the issues related to choosing particular samples when trying to select a representative sample.  

All Khan Academy content is available for free at www.khanacademy.org

Learning Activity 1

Focus: Drawing conclusions from data

Read the Roy Morgan Research report on mobile phone choices and use the information to answer the following questions.

How we choose a mobile network: quality versus price in capital cities, country
areas, and across the ages

Questions

1. How many people were sampled in the survey conducted?
2. What criteria were used to select the sample?
3. Which part of the population chooses a mobile phone service based on cheaper prices?
4. What can telephone services learn from the results of the survey?

Click here to check your answers

Learning Activity 2

Focus: Drawing conclusions from data

Read the Roy Morgan Research report about which consumers buy nail polish and answer the following questions.

Technicolour dreaming: Gen Z women most likely to buy nail polish

Questions

1. How many people were sampled in the survey conducted?
2. Which companies would be interested in the consumer profile constructed from the data?
3. Calculate the national average from the data in the column graph.
   

Click here to check your answers

Learning Activity 3

Focus: Making predictions from data

At the 2012 Olympics, Australia came tenth in the medal tally, which is based on number of gold medals awarded. Countries who win lots of medals, like China and the USA, have larger populations than Australia.

Complete the activity.

Is Australia the greatest Olympic sporting nation?

You can download the worksheet and the solutions from the bottom of the web page.

Questions

1. Do you think a country that has a large population has an advantage in winning medals at the Olympics?
2. Do you think the list of countries is a large enough sample to be confident your conclusion applies to all countries that compete in the Olympics?
   

Check your Understanding of Big Idea 4 and the entire Data and Statistics module

The purpose of Big Idea 4 was to help you understand how to;

• draw conclusions and make predictions based on evidence from the data set and
• make inferences about larger populations from data samples

Over the entire module you will have learned to;

1. Describe and find different types of data that are collected by businesses, government, service industries, communities and individuals (Big idea 1)
2. Recognise the difference between categorical and numerical data (Big idea 2)
3. Extract data from tables and graphs (Big Idea 2)
4. Compare two related data sets represented in a graph (Big Idea 3)
5. Describe the relationship between selected bivariate data (Big Idea 3)
6. Describe the general features of a data set including mean, median, mode and range (Big Idea 3)
7. Use features of a data set to describe the data (Big Idea 3)
8. Draw conclusions and make predictions based on evidence from the data set (Big Idea 4)
9. Make inferences about larger populations from data samples (Big Idea 4)

Extension and Additional Resources

The Australian Bureau of Statistics has fantastic resources that can be used to learn more about statistics and has ideas for teaching statistics on the website.

Bringing Data to Life in the Classroom

The resources are sorted according to Year Levels and Subjects according to the Australian Curriculum.

Additional resources

“What Graph or Display to Use When” is a summary of different tables and graphs. The document can be downloaded from the link in the AC Support menu.

Glossary of Statistical Terms

Steps on Running a Survey not only sets up how to run a survey but also gives examples of data that may be collected and provides examples of graphical representations that may be constructed from the data.