ACARA v9 CONTENT DESCRIPTION “acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables, to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data”
Builds on earlier work collecting information and sorting it into categories, and on counting and comparing. Year 5 turns that into handling data properly: deciding what kind of data a question produces, organising it into a table, and showing it in a column graph or a dot plot so that patterns can be seen at a glance. Reading a display back, and checking that it answers the original question, is the start of thinking statistically, and it leads into the line graphs and full investigations of later units.
Numerical and categorical data
Data is the information collected to answer a question, and the first thing to notice is what kind it is. Categorical data sorts things into groups, like favourite colour or type of pet, where each answer is a label rather than a number. Numerical data is counted or measured, like the number of pets a child owns or a height in centimetres, where each answer is a number that can be ordered and compared. Some categories even have a natural order, such as small, medium and large, and these are called ordinal. Knowing the kind of data decides how it should be organised and which display will show it best.
Numerical or categorical
Decide whether each variable is a number or a group.
Is favourite colour numerical or categorical?
Organising data in a table
Once data is collected it needs to be organised before it can be understood. A frequency table is the simplest tool: each different value or category is listed, and beside it the number of times it occurs, often counted first with tally marks. Organising raw answers this way turns a messy list into a tidy summary, where the most common and least common values stand out immediately. A good table is also a check on the data itself: gaps, impossible entries or miscounts are far easier to spot once everything is gathered into rows and totals rather than scattered through a list.
Organising data in a table
A frequency table lists each value with its count.
Each pet is listed with the number of children who chose it. Reveal the counts.
Showing data in a column graph
A column graph turns a frequency table into a picture. Each category gets its own column, and the height of the column shows how many fall into that category, so taller means more. Because the eye compares heights quickly, a column graph makes differences obvious in a way a table cannot: the tallest column is the most common answer at a single glance. Columns are drawn with equal widths and even gaps, and a clear scale up the side, so that the heights can be read off and trusted. Column graphs suit categorical data, where the columns are separate groups.
Showing data in a column graph
Taller columns mean more in that category.
The height of each column shows how many chose that pet, so the tallest column is the most popular.
Dot plots for numerical data
A dot plot is a neat way to show numerical data. A number line is drawn along the bottom, and one dot is placed above the matching value for each piece of data, so repeated values build into a stack. The result shows at once where the data clusters, how spread out it is, and which value occurs most often. Dot plots keep every single data point visible, unlike a column graph that groups them, which makes them ideal for small sets of counted or measured numbers. The taller the stack of dots, the more often that value appeared.
Dot plots for numerical data
One dot per child, stacked over its value.
Each dot is one child and the number is how many siblings they have; the stack over four is tallest, so four was the most common.
Reading and checking a display
A display is only useful if it can be read back accurately. Reading a column graph or dot plot means matching a column or stack to the scale to recover the number it stands for, and comparing heights or stacks to say which is most, least or the same. It also means checking that the display actually answers the question that was asked: the right data, a sensible scale, and clear labels. A graph with a missing label or a misleading scale can suggest the wrong conclusion, so reading carefully and questioning what is shown are as important as drawing the display in the first place.
Reading and checking a display
Recover the numbers a display stands for.
Use the table, column graph and dot plot above to answer.
From question to answer
Handling data is a journey from a question to an answer. Decide what kind of data the question needs, collect and organise it into a table, choose a display that suits the data, and then read the display to draw a conclusion. A column graph compares categories, a dot plot shows the shape of a set of numbers, and both make a summary that can be checked against the original question. With these habits a child can turn a pile of raw answers into a clear, honest picture, ready for the line graphs and investigations that the rest of Year 5 brings.
Quick self-check
1. A child's favourite sport is an example of...
2. The number of pets a child owns is...
3. A table that records how many times each value occurs is a...
4. In a column graph, the height of each column shows...