Key Stage 3 science · Working scientifically

KS3 science data: graphs, conclusions and evaluating errors

Collecting results is only half of an investigation. In Key Stage 3 pupils learn to present data in tables and graphs, calculate with it, look for patterns, draw a conclusion that is backed by the numbers, explain it with scientific ideas, and judge how far the data can be trusted. They finish by asking what new question their results raise, which is how real science moves on.

Analysing and evaluating data, explained

Pupils begin by organising results. A results table has the independent variable in the first column, the dependent variable next, units in the column headings rather than repeated in every cell, and a column for the mean when readings are repeated. They apply their maths: calculating means and ranges, working out percentages, rearranging a simple formula and converting units.

Choosing the right graph matters. When both variables are numbers that can take any value in a range, such as mass and extension, a line graph or scatter graph is used: the independent variable goes on the horizontal axis, the scales are even, the axes are labelled with units, and a line of best fit is drawn. That is a smooth line or a ruled straight line that follows the trend, with roughly as many points above as below it. It is not a dot-to-dot line. Where one variable is a category, such as types of soil, a bar chart is more suitable. A result that does not fit the pattern is called anomalous. Pupils should mark it, think about why it happened and say whether they would repeat the reading.

The conclusion is the answer to the original question, backed by the data. A strong one states the pattern with figures (“each extra 100 g added about 2 cm”), says whether it supports the prediction, and then explains why using scientific knowledge. Pupils are also taught that two things changing together does not always mean one causes the other. Sunburn and ice-cream sales rise together, but neither causes the other: both go up in sunny weather.

Evaluation looks at the quality of the evidence. Random errors cause readings to scatter above and below the true value, for example reading a scale slightly differently each time. They can be reduced by repeating and taking a mean. Systematic errors push every reading the same way, such as a ruler that starts at 1 cm instead of 0, and repeating does not fix them. Pupils suggest specific improvements and finish with a further question, such as what happens when the masses are much heavier.

Words your child will hear

Anomalous result: A reading that clearly does not fit the pattern of the rest of the data.
Line of best fit: A line drawn through a graph’s points to show the overall trend, not joining the dots.
Mean and range: The mean is the total divided by the number of readings. The range is the highest minus the lowest.
Correlation: A relationship between two variables where they change together. It does not by itself show that one causes the other.
Random error: Unpredictable differences that scatter readings above and below the true value.
Systematic error: An error that moves every reading the same way, such as a zero error on an instrument.
Conclusion: The answer to the investigation’s question, backed by the results and explained with science.

What the National Curriculum says

In Key Stage 3, pupils should be taught to:

Apply mathematical concepts and calculate results
Present observations and data using appropriate methods, including tables and graphs
Interpret observations and data, including identifying patterns and using observations, measurements and data to draw conclusions
Present reasoned explanations, including explaining data in relation to predictions and hypotheses
Evaluate data, showing awareness of potential sources of random and systematic error
Identify further questions arising from their results

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

Try it: analysing results from a spring

A pupil hangs masses on a spring and measures how far it stretches. Mass (g) and extension (cm): 100 g, 2.0 cm; 200 g, 4.1 cm; 300 g, 7.5 cm; 400 g, 8.0 cm; 500 g, 10.1 cm. The prediction was that more mass means more extension. What does the data show?

Plot the graph. Mass is the independent variable, so it goes on the horizontal axis (0 to 500 g). Extension is the dependent variable, so it goes on the vertical axis (0 to 12 cm). Label both axes with units.
Look for the pattern. Apart from 300 g, each 100 g adds about 2 cm: 2.0, 4.1, then 8.0 and 10.1 at 400 g and 500 g. The point at 300 g (7.5 cm) is the odd one out, because the pattern suggests about 6 cm there.
Draw the line of best fit. A ruled straight line starting at the origin passes close to most points, with the 300 g point clearly above it. Mark that point as anomalous rather than bending the line to reach it.
Write the conclusion with numbers. Extension increases in proportion to mass: the ratio of extension to mass is about 0.02 cm per gram (for example, 10.1 ÷ 500 = 0.0202). This supports the prediction, and goes further than it: the extension does not just increase, it increases at a steady rate for these masses. Doubling the mass, from 200 g to 400 g, roughly doubles the extension, from 4.1 cm to 8.0 cm.
Evaluate. A likely cause of the anomaly is a one-off mistake, such as misreading the ruler or writing down the wrong number at 300 g. Repeating that reading would test this. The small scatter of the other points, such as 4.1 cm rather than exactly 4.0 cm, is the kind of random error that repeating and taking a mean would reduce. If all the readings were consistently 1 cm too large, that would suggest a systematic error, such as the ruler not being lined up with the spring’s starting point. A further question: does the spring keep stretching steadily if much heavier masses are used?

Extension is directly proportional to mass for these readings (about 2 cm for every 100 g), supporting the prediction. The 300 g reading is anomalous, probably a one-off misreading, and should be repeated.

Common mistakes and how to help

Joining the dots on a graph with a ruler

Pupils treat each point as perfectly exact, and join them as in a connect-the-dots puzzle.

What helps: Explain that each point has some error. The line of best fit shows the trend. Ask “where would the next reading probably fall?”

Writing a conclusion that just repeats the results

“It goes up” feels like an answer, but it only describes. Pupils often do not realise they are expected to use numbers and science ideas.

What helps: Use three prompts: what is the pattern, with numbers; does it match the prediction; and why does it happen? A good conclusion answers all three.

Believing repeating the experiment removes all error

Pupils learn that repeating gives a more reliable mean and assume it deals with every kind of mistake.

What helps: Contrast the two kinds of error. Taking a mean helps with random scatter, but if every reading is shifted by the same amount, the mean is shifted too.

Assuming correlation means cause

When two graphs rise together it feels natural to assume one drives the other, especially in headlines.

What helps: Ask what else might cause both, as with sunshine, sunburn and ice cream. In an investigation, only controlling the other variables lets you say what caused the change.

How to help at home

Graph something at home. Track a number over a week, such as the daily minimum temperature outside, how many minutes of daylight there are, or the time it takes to run a lap of the garden. Ask your child to choose the graph type and explain why.
Say the conclusion in a sentence. After any practical, ask for one sentence that has a number, a link back to the prediction and a reason. “Each extra 100 g stretched it about 2 cm, as I predicted, because a bigger force pulls the spring further” is a model answer.
Hunt for graphs in the news. Look at a graph in a newspaper or on the TV news together. What is on each axis, does the scale start at zero, and does the headline claim more than the data show? Spotting misleading scales is a useful life skill.
Compare repeated readings. Drop a ruler for a friend to catch and note where they catch it, five times. Compare the readings, find the mean and range, and discuss which reading looks odd and why.

Builds on

Years 5 and 6: Working scientifically

Leads on to

Key Stage 4: The development of scientific thinking
Key Stage 4: Experimental skills and strategies
Key Stage 4: Analysis and evaluation
Key Stage 4: Units, symbols and nomenclature