CSER Statistics - Content in Action
See also: cser-content-in-action, teaching-mathematics, v9-learning-areas
Related resources
- What's in a name? examine trends in the names of students in the class and trends in popular names from 2017 and 1957. They look at data associated with these names and explore the use and significance of the mode as a measure of central tendency.
- Sport salaries These units explore variations in the salaries of NBA players. Using real-world data, they calculate means and medians, draw graphs, compare findings, and investigate the implications of random sampling.
- Algorithmic thinking: Data visualisation These units show how computation complements, extends, and enriches traditional mathematical methods and demonstrate the methods with which mathematicians work in the real world.
- The taste of water Students test a common claim (that bottled water tastes different to tap water) and collect experimental data. They determine the statistical significance of their findings. This sequence introduces students to informally conducting experiments to test hypotheses.
- Questionnaire design guide (ABS)
- recent reports by WWF International Links to an external site. and the Plastic Free Foundation
Introduction#
Statistics provides ways of understanding and describing variability in data and its distribution. Statistics provides a story, supports an argument and is a means for the comparative analysis that underpins decision-making and informs a process for making informed judgements.
Statistical literacy
- understanding of statistical information and processes
- awareness of data
- ability to interpret, evaluate and communicate statistically
- provides a basis for critical scrutiny of accuracy/validity of arguments/representations
Sources of data IoT etc. Growing.
Connections with Digital Technologies could be useful - year 8 e.g. AC9TDI8P01
Key Terms#
| Term | Definition |
|---|---|
| Bivariate data | Bivariate data is the data for two variables, such as temperature and sunglasses sales, and shows how the variables are related. |
| --- | --- |
| Census | A census is a collection from a whole population rather than a sample of the population. The census is run every 5 years in Australia. |
| Dependent variable | The dependent variable is the variable that depends on another value, for example, the distance travelled is dependent on the amount of time spent driving. |
| Distribution | A distribution refers to how often data values occur. Often the plot of the distribution reveals a characteristic shape e.g. data may be normally distributed, or positively skewed. |
| Independent variable | The independent variable is the variable that is manipulated in the experiment or data collection to investigate the effect on the dependent variable. For example, time is the independent variable when travelling. |
| Measures of central tendency | Measures of central tendency include the mean, median and mode. The mean (average) is found by adding all the data values and dividing by the number of values. The median is the middle value when all data values are listed in order. The mode is the data value that occurs the most. |
| Population | A population is the complete set of individuals, objects, places etc. about which we want information. |
| Sample | A sample is a selection from the population. The aim is for the sample to be representative of the population, so it needs to be random. |
| Statistical investigation | A scientific method of gathering data in order to seek meaning from observed phenomena and inform decisions and actions. |
Everyday matho#
- reading tables for school/workflows
- census - reading population data
- interpreting graphs in news media
- data representations of phone and battery usage
- engagement metrics
- nutrition & cooking
Guide#
Statistical skills allow
- determine the data needed to answer questions
- formulate data collection questions and strategies to acquire and record data
- represent categorical data using digital tools
- compare and interpret data using frequencies and common features which link to the questions posed
- use the data to make informed decisions.
Fundamentals#
| Structural component | Description |
|---|---|
| Statistical measures | Of spread and central tendency |
| Representations | Graphs, tables, infographics |
| Data types | Continuous and discrete; categorical and numerical |
Terms
| Term | Definition |
|---|---|
| descriptive statistics | describe characteristics of a data set |
| inferential statistics | used to make inferences/guide decisions |
| categorical data | data that can be sorted into groups or categories |
| numerical data | data that can be measured or counted |
| discrete data | data that can only take certain values, typically whole number values |
| continuous data | data that can take any value within a range |
| statistic | A single number that describes a particular property of a data set |
Averages
Attempt to represent a common or typical value in a data set. Three different ways
| Type of average | Description |
|---|---|
| mean | Sum of all values divided by the number of values. Sensitive to outliers. |
| median | Middle value when all values are listed in order. Divides a sample in two. Quartiles divide a sample in 4. The lower quartile is the median of the bottom half. |
| mode | Most common value. e.g. most commonly sold product (size of shoe) |
Measures of dispersion used to understand the spread/variation. Most common is the range, interquartile range (IQR) and standard deviation. An outlier is a value that is much larger or smaller than the other values in the data set.
Graphs and tables
| Type | Description |
|---|---|
| Frequency table | A frequency table is often used before (or in conjunction with) constructing a table or a graph. |
| --- | --- |
| Dot plots | A dot plot is a simple method of showing the frequency distribution of discrete numerical data. |
| Picture graph | A picture graph is used to represent the frequency distribution of categorical data. In addition, picture graphs can reinforce the idea of 1-1 correspondence with younger students. |
| Bar and column graph | Bar and column graphs are used to represent the frequency distributions of categorical data. |
| Pie graph | Pie graphs are a useful way of illustrating part-whole relationships. |
| Histograms | Histograms are used to represent the frequency distribution of continuous numerical data. |
| Line graphs | Line graphs are appropriate when the independent variable is continuous. |
| Scatter graph | A scatter graph shows the relationship between two numerical variables. Scatter graphs can be used with discrete or continuous numerical variables. |
| Stem-and-leaf plot | A stem-and-leaf plot provides a compact visual representation of a data set. Each data value is broken into a stem (usually the first digit of the number) and a leaf (the number's last digit). |
| Box plot | Box plots (also known as box and whisker diagrams) provide a visual representation of a data set that shows: - the maximum score - the upper quartile - the median (not the mean!) - the lower quartile - the minimum score. |
Statistical Investigation#
Process involving posing a question/defining purpose for data collections, acquiring it, organising and displaying to allow for analysis/inferences/conclusions
Misunderstandings#
Common misunderstandings in Year 7 to Year 10 statistics can include the following concepts where students may exhibit the reasoning described.
- When reading scales and tables of data, students may make assumptions rather than read the provided information.
- Believing that an average is a typical score that can be calculated in various ways, for example, the mean, mode or median. It is not just the mean.
Digital technology tools#
- Our world in data Links to an external site. provides research and data to make progress against the world's largest problems. The site is a project of the Global Change Data Lab. Data is represented in charts, maps and tables and is available to download. Topics include health, demographics, agriculture and energy and environment. In addition, a Teaching Hub- Links to an external site.provides links to resources for teaching and learning about global development.
- Australian Bureau of Statistics - Data explorer
- Links to an external site. - an interactive free online tool that presents data in a searchable, flexible and dynamic way. Data Explorer (in Beta 2023) allows you to search and filter ABS statistics and export to .csv format.
- Gapminder Links to an external site. provides teaching materials- Links to an external site. to explore global issues through analysis of statistics. Dollar street, Bubble charts, Income mountains and Trends are a few of the interactive resources provided. Gapminder tools are available to be downloaded to be used offline.
- Australian Data Science Education Institute Links to an external site. (ADSEI) provides datasets modified for classroom use and lesson ideas.
Challenges#
Spurious correlations#
Have students investigate a statement that involves an implied connection between two variables by collecting and representing data and discuss if the comparison has any correlation
- People who own pets that are carnivores (For example: dog/cat) prefer meat lovers pizza.
- People who live on the north side of the city have more children in their families.
- Tall people run faster than short people.
- People who exercise more have a higher risk of skin cancer
Sports shoe sale challenge#
Have students develop a model of what influences secondary students to buy particular shoes. Developing a mathematical model.
The class brainstorms 10 factors and then whittle it down.
Scaffolding knowledge#
Both examples source data from somewhere to then drive student exploration of the data set - secondary data set to explore analysis and display of the data.
- interpret and compare data sets
- interpret and analyse graphs
Flatback turtle population#
Uses data trom the Digital technologies Hub's data science resources
Draws on various links to other areas of the Australian Curriculum. e.g. the sex of turtles depends on the temperature of the sand when the turtle hatches
Concrete#
Students download and begin to work with the data. Can't collect the data themselves, so download.
Reflection questions
- How do students discuss the use of the graphs and who would use them?
- What information do students interpret from the graphs?
- What statistics do students use to summarise data?
- How do students use statistics to make sense of the data?
Representational#
Time to construct plots to display the data. - explore different representations
Pose questions
- What are some ways you could organise data?
- How can you organise data in a visual way?
- What are some ways you could summarise data?
Reflection questions
- How do students select, create, and use appropriate graphical representations of data?
- How are students grouping the data?
- Are they able to create and interpret frequency tables?
- How do students compare variation in attributes?
- How do students connect features of the data?
- How do students investigate techniques for data collection?
Abstract#
Commence using statistics to describe the data.
Pose questions
- What percentage of time is the sand at a viable temperature for Flatback turtle hatchlings? What percentage of time is the sand at, or close to, the pivotal temperature?
- When is the most suitable month or months for turtles to nest at the particular location?
- What type of graph could be used to show changes in temperature over time?
- How could the graph clearly show when the eggs are unviable? That is, when the temperature is above or below- ?
- Are you able to identify any outliers in the data?
Reflection questions
- What method(s) do students use to find the mean, median, mode, and range of the data?
- How do students compare the measures of central tendency for multiple data sets?
- How do students determine which measure of central tendency to use to describe their data effectively?
- Do students recognise the limitations of the model, median and mean?
- Do students recognise the impact of shape of distribution on measures of central tendency?
Great Barrier Reef#
From the CSIRO website.
Concrete#
Data download. CSIRO provides data at two levels, allowing some differentiation. Recommended students are provided that dat set as a spreadsheet.
Pose questions
- How often was the data collected?
- What was the mean \(CO_{2}\)
- concentration for the equilibrator data and the interpolated data?
- What was the mean pressure for both the equilibrator data and the atmospheric data?
- What was the mean sea temperature at the surface?
- What was the mean salinity?
- When do the wind direction and speed change? Why might this be the case?
Reflection questions
- How do students compare data displays using mean, median and range?
- How do students conduct statistical investigations?
- How do students summarise the data?
Representational#
Construct various appropriate plots.
Pose questions
- What dates did you select? Why did you choose this range?
- Do you think you chose the right amount of data to represent? Why?
- How did you choose to represent the data on your stem-and-leaf graph? Using rounded or decimal data?
- Why did you choose to round or not round your data?
- How do you think this affected your stem-and-leaf and box plot graphs?
Reflection questions
- Are students able to represent the data using a back-to-back stem-and-leaf graph?
- Are they able to find the range, median and interquartile ranges required to make a box plot graph?
- Are students able to use the range, median and interquartile ranges to create a box plot?
Maths investigations#
Statistical investigation (7 & 8)#
Survey design - provides some of the content descriptions and a couple of images, and a statistical-investigation-checklist
- teacher assist selection of topic of interest
- Students can work in small groups to develop survey questions
Pose questions
- What types of data did you get in this investigation?
- How did you record the data as you collected it?
- What sort of data display is appropriate for the information you collected?
- What are observational and experimental data in statistics?
- How can outliers be determined in a dataset?
- What statistics were useful?
Reflection questions
- Was the research question clearly defined?
- Were the data collection questions clear and unambiguous?
- Did the data collection questions provide the data needed to answer the research question?
- Was the data presented in an organised manner?
- Was the data displayed in an appropriate manner?
- Was the data interpreted correctly?
- How did students justify inferences from their sample data to the population?
- How did students justify that their sampling techniques were fair and did not contain bias?
How people use their time (7 & 8)#
Comparing real-life data about time use - comparing Australian data to that of other countires
Year 7 - use data from Our World in Data Links to an external site., students will consider trends in how much time is spent on different categories of time use -- analysing the data
Pose questions
- Which measure of central tendency is the most useful for summarising your category?
- How did you organise and display your data?
- How can you describe the distribution of your data?
- What comparisons can you make between the two categories of time usage?
- How does Australia compare to the rest of the world?
Year 8 - gather and compare. Students conduct their own survey and compare with data from the ABS- "How Australians use their time
Pose questions
- How do the sampling techniques used by Our World in Data and The Australian Bureau of Statistics compare with your own sampling techniques?
- For your chosen categories, how can you describe the distribution of data from your primary data and from secondary sources?
- What conclusions can you make about how sample size and sampling techniques can affect the distribution of data?
Reflection questions
- How did students describe the shape of distribution?
- How did students explain their choice for the most suitable measure of central tendency?
- How did students explain the effects of sampling techniques on the distribution of data and measures of central tendency?
Rising house costs (9 & 10)#
As working conditions change with new technology, many occupations no longer need to be working in an office. This has seen a change in population density as many people move out of the capital cities. In this activity, students will collect data on property prices in different regions of New South Wales. They will represent and analyse the data using appropriate methods and draw conclusions based on their research.
Statistics in the media (9 & 10)#
Informed decision-making depends on the ability to evaluate information presented in the media, assess the reasonableness of claims, and identify any biased reporting. In this activity, students will investigate media representations of public opinion around the environmental issue of plastic pollution