Represent collected data: Year 7: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M7ST02

Numeracy Progression: Interpreting and representing data: P5

At this level, students expand their knowledge of numerical data displays. Students draw or use digital software, such as Geogebra, Desmos or Excel, to create their graphs or charts. Give ample opportunities to practise drawing stem-and-leaf plots, especially choosing the correct stems. Then, explain the different uses of bar graphs and histograms, referencing discrete and continuous data. It is helpful to refer to continuous data as 'measured' and discrete as 'counted'.

It is useful to show a variety of public transport timetables as examples of stem-and-leaf plots in the real world. Collect data from the class about what time they leave home for school in the morning and arrange this into a stem-and-leaf plot on the board. Students can collect their own data to replicate this process. At this level, students should also be producing dot plots. Students can collect information from their peers about the types of extra-curricular activities they participate in and organise this into a dot plot.

Once students can produce plots, demonstrate how to describe and compare data, and the way it is distributed. Students should look to the shape of the distribution, identify the centre spread and know how to identify outliers. Encourage students to attempt to explain the effects of outliers on measures of central tendency.

Show students how to determine the mean, median and mode as well as the data range, and connect what they mean and know about averages and the way data may be spread. This should be estimated visually from the shape of the distribution and calculated numerically from the dataset. Ask students to mark an estimation of where the median and mean is on the distribution based on the skew and to compare the mean and median to predict the presence of outliers.

Explicitly use the language of statistics, so that students are clear on the differences between mean, medium and mode and what they tell us about the data. Other terminology includes frequency, peaks, gaps, clusters, skewness, symmetrical, bimodal, spread and variation.

The vocabulary of statistics should be embedded in the classroom language. Students use this language to describe the data. However, variation is not introduced explicitly, so students could describe this qualitatively.

Once comfortable, students can be introduced to back-to-back plots and the concept of comparing datasets. If providing data with meaningful context, students can work with the data in an engaging manner, helping these statistical exercises to be less procedural and allowing for connections to be made.

Teaching and learning summary:

Revise and extend different types of data displays and their characteristics.
Introduce stem and leaf plots:
- What type of data are they used for?
- Identification of the 'stem’.
- When would you use a stem and leaf plot?
- Back-to-back stem and leaf plots.
Discuss the displays produced and the inferences that can be made.
Show how calculations can be made, including range, mode, median and mean.
Make comparisons between different data displays.
Consistently use new terminology when describing displays, including skewness, spread, variation, frequency, outliers.
Use graphing software, such as Geogebra, Desmos and Excel, to quickly produce displays.
Discuss the effect of outliers on mean and median.

Students:

know a variety of data displays and what they are suitable for
identify the stem and construct a stem-and-leaf plot
make accurate inferences from plots and identify characteristics for different examples
use a display to make statistical calculations such as mean, median, mode and range
construct back-to-back stem-and-leaf plots, dot plots, bar graphs and histograms
compare populations using statistical language consistently.

Some students may:

have difficulty identifying the stems in a set of data and therefore use the wrong leaves.
not pay close attention to the key, and misrepresent 3|2 as 32 when it is intended to be 3.2 or 3200.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to describe data and calculate the summary statistics.
We can select an appropriate data display for the dataset.

Why are we learning about this?

Every five years, the ABS collects a massive amount of data to understand more about Australia and its residents. This data is used in many ways and helps a range of organisations to make sensible decisions based on the most up-to-date information. The people collecting this data think very carefully about how to present it in the most informative way. How well do you know your local community? Try conducting a mini census for yourself. You’ll learn more than you think from a small amount of data.

What to do

Do you love a particular sport? Are you interested in plants or animals? Or maybe food is your passion? Think about something that’s important to you and that you’re passionate about, and decide on a relevant data point to collect.

Here are some examples:

number of different plant species in a garden
favourite carbohydrate (bread, rice, pasta, couscous etc.)
number of sports matches attended this year
time spent cooking dinner each night
number of household pets.

Choose a topic and write it as a question. For example, how many pets do you have?
Think about who you will ask. Try the neighbours in your street. To introduce yourself, you could write a short letter explaining your project and leave it in their letterbox or ring the bell and ask them in person.
Create a table to organise the data you will collect. Think about how many rows and columns you need, including headings.
Collect your data.
Record the answers into a table.
It’s time to describe and display it. Ask yourself whether the data you collected is categorical and if it is, could it be logically ordered. If the data is numerical, consider whether it is discrete or continuous.
Think about which data display most appropriately fits this kind of data. Also, consider which summary statistics would be useful to calculate. Ask yourself which statistics are meaningless with categorical data, whether the data is skewed and if there were outliers.
Finally, report back on your findings to the participants in the survey. Present the graph along with the statistics and make some comments about what you learnt from the data. Ask the participants to assess how informative your data display and statistics were.

Now you’re ready to assist the ABS with their next census!

Success criteria

I can describe the data I’ve collected and calculate the summary statistics.
I can present my data with a useful display.

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