Tables, charts, and graphs
Identify measurement-table headings, choose graph types, interpret axis labels, coordinates and even scales, explain fitted-line conventions and prediction limits, and calculate straight-line gradients from supplied points.
What a learner can do afterwards
- Identifies the quantity and unit in a measurement-table heading.
- Chooses graph types, identifies axis labels and coordinates, reads even scales, and explains limits of graph-based conclusions.
- Explains straight-line fitting conventions and calculates or interprets a gradient using supplied points or units.
1 · Read
Headings identify what a column records. For a measurement with a unit, include quantity and unit: Mass / g or Mass (g). Here g means grams, s means seconds, cm means centimetres and N means newtons, a force unit. Put numerical readings in rows. Category headings such as Colour and count headings such as Number of plants need no separate measurement unit.
Zara records spring length under added weight. Her headings are Weight / N and Spring length / cm. Her rows pair 0 with 8, 2 with 11, and 4 with 14. Each row keeps one weight with its measured length. Weight is a force measured in newtons, not a mass measured in grams.
Bar charts compare categories, such as favourite pets. A line graph can connect readings in time order to show change. A scatter graph plots paired measurements, such as leaf length and width, without joining separate observations. For a spring investigation, plot added weight horizontally and length vertically, then inspect the pattern before fitting a line.
Label numerical axes with quantity and unit. Put time or the quantity you change on the horizontal x-axis, and the measured response on the vertical y-axis. In (x, y), read x first. Locate both values, then mark where they meet. Equal distances on an axis mean equal changes in value. The axes may use different steps. Halfway between 4 and 8 is 6.
When points follow an approximately straight trend, use a ruler to draw a straight line through the middle of the scatter. Consider the distances of points on both sides. Equal numbers above and below are not enough on their own. The line need not touch every point or pass through zero. Use two well-separated points on the fitted line for its gradient; they need not be recorded observations.
Gradient = change in y divided by change in x. Subtract both coordinates in the same order. Gradient units are y-units per x-unit. A negative gradient means y decreases as x increases. For spring length against weight, cm/N means centimetres of length change per added newton. A gradient describes change, not the total length.
A straight line passes through (1, 6) and (4, 12). The y-change is 12 - 6 = 6 and the x-change is 4 - 1 = 3. Its gradient is 6 / 3 = 2. If x is weight in N and y is length in cm, the gradient is 2 cm/N.
A curved pattern may need a curved model. An upward scatter trend means larger x-values tend to occur with larger y-values; it does not prove that x causes y. A fitted line gives estimates, not exact future readings. Predictions outside the measured range have less support because the relationship may change there.
Keep table values paired, label numerical axes with units, choose a graph for the question, and calculate a straight line's gradient as y-change divided by x-change.
The lesson revisions, questions, worked solutions and flashcards were written for this dataset.
The readings, questions and flashcards were written for this dataset.
More to read
Keep each pair together
A spring investigation records two values for each test. Suppose a weight of 1 N gives a spring length of 9 cm, and 3 N gives 13 cm. Put Weight / N and Spring length / cm above the columns. Keep 1 beside 9 and 3 beside 13. Sorting the two columns separately would destroy the observations.
A heading such as Length (cm) also identifies a quantity and unit. The slash format is the convention used in this lesson, not the only understandable format.
For plotting, put added weight on the horizontal axis and spring length on the vertical axis. The first observation becomes (1, 9). Check each plotted pair against its table row.
What should the graph show?
Start with your question. Comparing beetle, snail and woodlouse counts calls for separate category bars. Following temperature readings through an afternoon calls for a graph with time horizontally and temperature vertically. Connecting those readings helps readers follow their order.
Leaf length and width are different. Each leaf supplies a pair of measurements, but the leaves have no measured sequence. A scatter graph gives each pair a point without joining different leaves.
Check scales before plotting. Equally spaced marks labelled 0, 4, 8 and 12 represent equal increases of 4. Halfway between 4 and 8 represents 6. The horizontal and vertical axes can use different numerical steps. Both need labels identifying their quantities and units.
Calculate a fitted line's gradient
Inspect the plotted observations before choosing a model. If they follow an approximately straight trend, draw a straight fitted line through the middle of the scatter. Consider distances from the line, rather than counting points on each side alone.
Choose two well-separated points on the line. A recorded observation is usable if it lies on that line. An observation away from it does not describe the fitted line's gradient.
For points (2, 15) and (6, 7), the y-change is 7 - 15 = -8 and the x-change is 6 - 2 = 4. Dividing gives -2. If y is temperature in °C and x is time in minutes, the gradient is -2 °C/min. The negative sign describes a temperature decrease.
Limits of a fitted trend
An upward scatter pattern means larger horizontal values tend to occur with larger vertical values. This is an association. The picture alone does not establish what causes what: another factor may affect both measurements.
A fitted line summarises observations and can supply estimates. A new observation need not land on the line. Curved data may need a different model, and a widely scattered cloud may give little support for a straight trend.
Predictions beyond the measured range require caution. Extending a line does not establish that the relationship continues there. State the range of the observations when explaining how much evidence supports a prediction.
2 · Watch
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Where it sits
Where this leads
15 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.