ACARA v9 CONTENT DESCRIPTION “select and construct appropriate representations, including tables, graphs, descriptive statistics, models and mathematical relationships, to organise and process data and information”
Builds on choosing tables and graphs to show a pattern. Here you also process the data: you compute descriptive statistics that summarise it in a single number, and you write a mathematical relationship that turns a trend into a rule. The skill is matching the representation to the data and the purpose.
Many ways to show the same data
A class audits home appliances for an energy-efficiency project. The raw readings begin as a table of numbers. A table keeps every exact value, but it is hard to read a pattern off rows of digits. Switch to a bar chart and the appliances rank themselves; switch to a line and a trend over time appears. No single representation is best for everything, so the first inquiry skill is choosing the one that fits the data and what you want to show.
Energy use of six household appliances
Yearly energy use, in kilowatt-hours, for six appliances. Start with the table, then switch to the bar chart to compare them at a glance.
In the table you compare numbers row by row. As a bar chart the comparison is immediate: the heater dwarfs the lamp, and the appliances sort themselves by size. The bar chart is the right representation when the purpose is comparing separate categories.
Summarising data with descriptive statistics
Sometimes you do not want every value, you want one number that stands for the set. These are descriptive statistics. The mean adds all the values and divides by how many there are. The median is the middle value once they are sorted. The range is the largest minus the smallest, a measure of spread. Each processes the data differently, so each tells you something different about it.
Standby power of six chargers
Standby power draw, in watts, for six phone chargers left plugged in. View the table, then the bar chart, and read off the spread of values.
The mean is 26 divided by 6, about 4.3 W, but charger F at 9 W pulls it up. The median, the middle of the sorted values, is 3.5 W, which sits among the typical chargers. The range is 9 minus 2, which is 7 W. The high outlier is exactly why the median and the mean disagree.
When a value breaks the pattern
Descriptive statistics can hide a single odd value, but a graph makes it stand out. A group measured the power a solar panel makes at rising light levels and expected a steady climb. Most points line up, but one sits far off the trend. On a graph that point is obvious at once, the first sign of a misread meter or a shaded panel to check before you trust the rest of the data.
Read the graph: find the reading that breaks the trend
Power output of a solar panel at six rising light levels. Five points climb steadily; one does not. Click the level whose reading does not fit.
Click the point that does not fit the pattern of the others.
From a trend to a mathematical relationship
When points climb in a straight line through the origin, the data is more than a trend: it is directly proportional. The solar panel makes a fixed amount of power for each unit of light, so power equals a constant times light, written power = k times light. That equation is the most compact representation of all. It is a model you can calculate with, predicting the output at a light level you never measured. Sorting which conclusions the data and its rule actually support is how you avoid claiming more than the model can show.
Test conclusions against the data and its statistics
Use the appliance audit and the solar-panel data above, with their descriptive statistics and the proportional rule power = k times light. Decide which conclusions the data actually supports.
Claim: The data, its descriptive statistics and its mathematical relationship support the statement being judged.
A bar chart is a good choice for comparing the energy use of separate appliances.
Doubling the light on the solar panel roughly doubles the power it makes.
For the chargers, the median represents a typical charger better than the mean does.
The mean charger power of about 4.3 W means most chargers draw close to 4.3 W.
The proportional rule will hold for any light level, however bright, with no limit.
Decide whether each statement is evidence for the claim, or not.
Why this matters
A table records data, a graph reveals its shape, descriptive statistics compress it to a few telling numbers, and a mathematical relationship turns a trend into a rule you can calculate with. Each representation organises and processes the data for a different purpose, and choosing well is a skill in itself. Engineers, energy analysts and climate scientists all depend on selecting the representation that turns raw measurements into knowledge.
Quick self-check
1. Six fridges use 110, 130, 140, 150, 160 and 270 kWh a year. Which single number best summarises the typical fridge here?
2. For the heater data 8, 9, 10, 11 and 12 degrees of rise, the range is found by...
3. A solar panel makes 50 W of power in full sun, 100 W in double the sunlight and 150 W in triple. Doubling the light...
4. You want to predict the solar power for a light level you never measured. The most useful representation is the...
5. You have time-of-day data and want to show how a room cools over an evening. The clearest representation for that purpose is a...