How to teach scatterplots and two-way tables
Year 10 (ages 15 to 16)
Scatterplots and two-way tables both explore the relationship between two variables: a scatterplot for two numerical variables (plotted as points), and a two-way table for two categorical variables (organised as counts in a grid).
How to teach it
- Start by plotting real paired data (e.g. hours studied vs test score) as a scatterplot, then describe the pattern in words before naming it.
- Introduce positive correlation, negative correlation, and no correlation as three distinct patterns, with a labelled example of each.
- Move to two-way tables: organise categorical data (e.g. sport yes/no by instrument yes/no) into the four combination cells, checking they sum to the total.
- Discuss strength (how tightly points cluster) and direction (positive/negative) separately when describing a scatterplot.
- Caution that correlation, however strong, does not by itself prove one variable CAUSES the other.
Common mistakes
- Describing a scatterplot's direction (positive/negative) but ignoring its strength (how closely the points follow the pattern).
- Assuming a strong correlation between two variables means one causes the other.
- Forgetting to check that a two-way table's cell counts add up to the stated total.
- Confusing a two-way table (categorical data, counts) with a scatterplot (numerical data, points).
Frequently asked questions
What does a scatterplot show?
A scatterplot shows the relationship between two numerical variables, with each point representing one pair of values. The overall pattern reveals whether the variables are positively associated, negatively associated, or show no clear association.
What is the difference between positive and negative correlation?
In a positive correlation, as one variable increases the other tends to increase too. In a negative correlation, as one variable increases the other tends to decrease. No correlation means there is no consistent pattern.
What is a two-way table used for?
A two-way table organises data by two categories at once (e.g. plays sport by plays an instrument), letting you read off the count or probability for any combination of the two categories directly.
What year are scatterplots and two-way tables taught?
In the Australian Curriculum these are Year 10 skills: constructing and describing scatterplots (AC9M10ST03), two-way tables (AC9M10ST04), and investigating bivariate data more broadly (AC9M10ST05).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.