ACARA v9 CONTENT DESCRIPTION “create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context”
A frequency table is tidy, but a graph is instant: a glance shows which category is biggest and how they compare. This unit takes the travel survey from the previous unit — walk 6, car 8, bus 4, bike 2 — and turns it into the two displays Year 3 uses most, the column graph and the picture graph. Creating a graph from data and reading a graph back are two halves of the same skill, and the curriculum asks for both, along with interpreting what a graph means in its context. Software can draw these graphs too, but the thinking is the same whether the bars are drawn by hand or by a spreadsheet.
Table to columns
A column graph shows each frequency as the height of a bar.
The frequency table from before becomes a column graph. Grow the columns to their counts.
From frequencies to columns
A column graph represents each category as a bar whose height is its frequency, so the taller the bar, the larger the count. Turning the travel table into columns makes walk, car, bus and bike into four bars of different heights, and suddenly the comparison that took careful reading in the table is obvious at a glance. The bars must share a common baseline and an even scale for the comparison to be fair — a taller bar should always mean more. This is the most important display in primary statistics, because it shows the shape of categorical data so clearly.
Read the column graph
Reading a column graph means comparing bar heights and reading their values.
Which travel method has the tallest column?
Which travel method has the tallest column?
Reading a column graph
Reading a column graph is asking the bars questions: which is tallest, which is shortest, and what value does each reach. The tallest bar is the most common answer, the shortest the least common, and the height read against the scale gives the exact count. These are the everyday questions a graph is built to answer, and being able to read them quickly is what makes a graph more useful than the raw table. Interpreting the display, as the descriptor asks, starts here — turning bar heights back into facts about the children surveyed.
The picture graph
A picture graph shows a count as a row of symbols, one per item.
A picture graph shows each count as a row of symbols. Reveal one symbol per child.
Picture graphs use symbols
A picture graph shows each count as a row of symbols, one symbol per item, so a row of six circles means six children. Picture graphs are friendly and concrete — the length of each row is the count — which makes them a natural first graph, closely related to the tally. Like a column graph, the rows must line up so their lengths can be fairly compared. The picture graph and the column graph show the same data in different ways, and comparing the two displays is part of what this unit asks: each makes the counts visible, one with height and one with length.
One symbol, many
A many-to-one picture graph uses a key, so each symbol stands for more than one.
The car row has 4 circles. How many children is that?
When counts are large, one symbol can stand for several. With this key, how many children does the car row show?
When one symbol means many
When counts get large, drawing one symbol per item becomes impractical, so a picture graph uses a key: one symbol stands for several. If the key says one circle equals two children, then four circles mean eight children, found by multiplying the number of symbols by the key. This many-to-one idea is where the multiplication of earlier units meets statistics, and reading such a graph means always checking the key first. It is a powerful idea because it lets a small, neat graph represent a large set of data without losing the comparison between categories.
Compare on the graph
A graph answers how-many-more and how-many-altogether by reading and combining values.
How many more children come by car than walk?
How many more children come by car than walk?
Comparing with a graph
Beyond reading single values, a graph answers comparison questions: how many more children come by car than walk, or how many were surveyed altogether. How-many-more questions are answered by finding the difference between two bars, and how-many-altogether by totalling them all. This is the addition and subtraction of earlier units put to work on real data, and it is exactly the kind of interpretation the curriculum means by understanding data in its context. A graph is not just a picture; it is a tool for answering questions about the group it describes.
Which graph fits?
Counts by category are best shown by a column graph or a picture graph.
Which display best shows favourite fruit of each child in a class?
Choosing the right display
Part of working with data is choosing a sensible way to show it. Counts by category — favourite fruit, pets per family, sport chosen — suit a column graph or a picture graph, because both compare categories clearly. A measuring tool like a thermometer or a ruler is not a display of categorical counts, and a line graph is for change over time, which comes later. Matching the display to the data is a real judgement, and comparing different graphical representations, as the descriptor asks, includes recognising which one fits. With columns, picture graphs, keys, comparison and display choice in hand, a child can both make and read graphs — and the next Statistics unit runs a full investigation from question to conclusion.
Quick self-check
1. On the travel column graph, which method has the tallest column?
2. A picture graph has a key of one symbol = 2 children. The car row shows 4 symbols. How many children?
3. How many more children walk (6) than ride a bike (2)?
4. In a column graph, the frequency of each category is shown by the column’s...
5. The best display for the favourite-fruit counts of a class is a...