Making muffins

Achievement objectives

S4-1: 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.

Required materials

See Materials that come with this resource to download:

• Making muffins activity (.pdf)
• Making muffins sales data (.xlsx)

Activity

A roadside "coffee cart" offers drinks and muffins for sale.

To make a healthy profit, they need to make just enough muffins to nearly sell out by the end of the day.

Use the sales figures for the past three months to suggest how many muffins they should make for a typical day.

The following prompts illustrate how this activity can be structured around the phases of the statistical enquiry cycle.

Problem

The problem section is about what data to collect, who to collect it from, and why it’s important.

• What is my investigation question? Why do I wonder about that? (The question might be framed as “I wonder how many muffins the cart operators should bake each day.)
• What variables should the cart owners consider? (Students might acknowledge that total sales and months (time) are key variables, but they might also separate weekdays and weekend days into two groups.)
• Is my question a summary, comparison, or relationship question? (The question involves a relationship between time and the number of muffins sold.)
• Why is my question important? (The answer will affect the profitability of the cart and whether it can operate financially.)

Plan

The planning section is about how students will gather the data.

• How will I go about answering this question?
• What data will I need? Is all the data available?
• How will I organise and display the data to look for patterns and relationships?
• Will I need to calculate some statistics? Which statistics? How will those measures be useful?
• Can I predict possible answers to my question even before I look at the data? How?
• What might my answer look like? (Students should realise that they need to provide a recommended number of muffins, supported by evidence and an argument.)

Data 

The data section is concerned with how the data is managed and organised.

• What format will I use to organise my data as I display it?
• What is the best way to look at trends over time? Why?
• What digital or written tools will help me organise my data? (Consider software for display since the data is in a spreadsheet that can be imported into online software.)
• How will I protect the data I gather or retrieve so it is safe?
• Is some data ‘dirty’ (untrustworthy)? How will I clean my data?

Analysis

The analysis section is about exploring the data and reasoning with it.

• Have I reflected back on my question so I am clear on what I am trying to find out?
• Do I get ideas about patterns, differences, relationships, and trends from just "eyeballing" the table of data?
• Are my important variables categoric, discrete, numeric, or continuous (measurements)?
• How can I display different sortings of my data to look for patterns, differences, relationships, and trends? 
• What tools will help me to display the data in different ways? What ways are appropriate to my data and help answer my question?
• How might I describe the trends over time? What language might I use to describe what I see? Are there trends, or is this the beginning of a seasonal pattern?
• Are there differences among statistics at different times in terms of centre, shape, and spread? Which measures should I use?
• What variation can I see in my data? What might be the causes of that variation?
• Can I make preliminary statements about my findings, starting with “I noticed that ...”

Conclusion

The conclusion section is about answering the question in the problem section and providing reasons based on their analysis.

• Have I answered my original question? If not, why not? (There should be a number of muffins per day recommended, possibly given for weekdays and weekends.) 
• How might I convince someone else that I have answered the question?
• What displays best show what I have found out? Explain why these displays are the best.
• Is my summary of findings clearly written so others can understand it?
• Have I used displays and measures to support my ideas?
• Do I go back to the context to suggest why the relationships and trends occur?
• What do I say about the limitations of what I have found out? What can I say, and what can’t I say?
• What strategies and tools proved the most useful in my inquiry?
• What other things have I learnt, and what further questions do I have?