ACARA v9 CONTENT DESCRIPTION “create and compare different types of data displays including column graphs and dot plots, and use displays to investigate the data and answer questions”
Collecting data fills a frequency table; the next step is to display it so the story is seen at a glance. Year 4 builds two displays, the column graph and the dot plot, both of which turn counts into heights. A table of pet counts becomes a row of bars, and the tallest bar is the most popular pet without any arithmetic. The purpose of a display is exactly this: to make comparison instant. Where the last unit organised data into numbers, this one turns those numbers into a picture that answers questions at a look.
Build a column graph
A column graph draws each category as a bar as tall as its count.
A column graph shows each category as a bar. Add the bars one at a time from the data.
Bars as tall as the count
A column graph draws one bar for each category, and the height of each bar is its count read off a frequency scale. Dogs with a count of six gives a bar reaching six; fish with three gives a bar reaching three. The bars stand apart because the categories are separate, and the scale up the side turns each height back into a number. Building a column graph is reading a table and drawing each count as a height, and it is the most common display a child will meet because comparing heights is so much faster than comparing numbers in a list.
Read the column
Read a bar's value by tracing its top across to the scale.
Read the value of Monday from the graph.
Reading a value from a bar
A display is only useful if it can be read back, and reading a column graph means tracing the top of a bar across to the scale. The bar for Monday reaching eight means eight; the tallest bar shows the largest value. This reading is the reverse of building: instead of turning a count into a height, it turns a height back into a count. Comparing bars answers questions directly — which is most, which is least, how many more — and a child who can read values off a graph can investigate the data without ever seeing the original table.
A dot plot
In a dot plot, each dot is one value stacked above its number.
Add a dot above a number for each value you record. Each dot stands for one.
One dot for each value
The dot plot is a second display, suited to single number values like how many siblings each child has. Each value is shown as one dot, stacked above its number on a line, so four dots above the number two means four children answered two. The height of a stack is its frequency, exactly like the height of a bar, but each dot stands for one piece of data, which keeps the individual values visible. Dot plots are quick to build by hand and make the shape of the data — where the values cluster — easy to see at a glance.
Table to graph
A column graph is a frequency table drawn as bars of matching height.
A frequency table on the left, an empty axis on the right. Draw the bars to match the counts.
A table and its graph agree
A column graph and the frequency table it comes from hold the same data shown two ways. Drawing the bars from a table makes this plain: each count in the table becomes a bar of that exact height, and nothing is added or lost in the change. This is worth seeing directly, because it shows a display is not new information but the same information made visible. Being able to move between a table and its graph, in either direction, means a child understands that the picture and the numbers are two faces of one set of data.
Which display fits?
Different data suits different displays: column graph, dot plot or table.
Which display best fits this data?
Choosing the right display
Not every display suits every kind of data. Categories like favourite pet or votes for a lunch option suit a column graph, one bar per category. Single number values, like the number of siblings, suit a dot plot, one dot per value. Data already sorted into groups with counts can stay in a frequency table. Choosing a display that fits the data is part of presenting it well, and a poor choice — like a number line for categories — makes the data harder to read, not easier. Matching the display to the data is a real Year 4 decision.
Parts of a graph
A graph needs a title, a category axis and a frequency scale to be read.
A graph needs labels to be read. Reveal each part to see what it does.
Every display needs its labels
A display can only be read if it is labelled. A column graph needs a title saying what it is about, a category axis naming each bar, and a frequency scale giving each bar its number. Without the scale, a bar is just a height with no value; without the category axis, you cannot tell what each bar counts; without a title, you do not know the subject at all. These labels are not decoration but the keys that make a display readable. With column graphs and dot plots built from tables, values read back off them, the right display chosen and every part labelled, a child can both make and interpret the displays that the next Statistics unit uses to answer real questions.
Quick self-check
1. In a column graph, the bar for dogs rises to 6 and is the tallest. The most common pet is...
2. In a dot plot, a stack of 4 dots above the number 2 means...
3. Data sorted into categories like favourite pet is best shown with a...
4. Why must a column graph have a labelled frequency scale?
5. A table shows walk 7. On the matching column graph, the walk bar should reach...