Bar charts and pictograms show how often each category occurs. A pie chart shows how a total is split: the whole circle is 360°, so each sector's angle is its share of 360°. A scatter graph plots two variables to show any correlation, and a line of best fit can be used to make estimates within the range of the data.
Charts and diagrams
- Pie chart angle = (frequency ÷ total) × 360°
- Degrees per item = 360° ÷ total
- Frequency from a sector = angle ÷ degrees per item
- Correlation: positive, negative or none
- Interpolation (within the data) is reliable; extrapolation (beyond it) is not
Bar charts and pictograms
A bar chart uses bars of equal width, with the height showing the frequency; read the scale carefully. A pictogram uses symbols, with a key saying how many items each symbol represents. A part-symbol represents a fraction of that amount, so with a key of 4, half a symbol means 2.
Drawing a pie chart
Divide 360° by the total to find the number of degrees for each item, then multiply by each frequency. For 40 people, each person is 9°, so 14 people who walk get 126°. Check that the angles add up to 360°, and draw each sector with a protractor.
Reading a pie chart
To find a frequency from a sector, divide its angle by the degrees per item. If 90 people were surveyed, each is 4°, so a 76° sector represents 19 people. A pie chart shows proportions, so you cannot compare actual numbers between two pie charts unless you know both totals.
Scatter graphs and correlation
A scatter graph plots pairs of values. If both increase together there is positive correlation; if one increases as the other decreases there is negative correlation; if there is no pattern there is no correlation. Correlation does not prove that one variable causes the other.
Lines of best fit and outliers
A line of best fit follows the trend, with roughly equal numbers of points on each side. Use it to estimate values within the range of the data, which is interpolation. Estimating outside the range, extrapolation, is unreliable. An outlier is a point far from the trend and may be ignored when drawing the line.
Worked examples
Example 1. 40 people were asked how they travel: walk 14, bus 9, car 13, cycle 4. Work out the pie chart angles.
- Degrees per person: 360 ÷ 40 = 9°.
- 14 × 9, 9 × 9, 13 × 9, 4 × 9.
Answer: Walk 126°, bus 81°, car 117°, cycle 36°.
Example 2. A pie chart shows 90 people. One sector is 76°. How many people does it represent?
- Degrees per person: 360 ÷ 90 = 4°.
- 76 ÷ 4.
Answer: 19 people.
Example 3. A pictogram uses a symbol to represent 4 books. One row has 3½ symbols. How many books is this?
- 3 × 4 = 12, and half a symbol is 2.
Answer: 14 books.
Example 4. As temperature rises, sales of hot drinks fall. What type of correlation is this?
- One variable increases while the other decreases.
Answer: Negative correlation.
Example 5. A line of best fit for revision hours and test scores is drawn for students who revised 2 to 10 hours. Why is it unreliable to use it to predict the score for 25 hours?
- 25 hours is far outside the range of the data.
- The trend may not continue.
Answer: It would be extrapolation, which is unreliable.
Common mistakes
- Using 100 instead of 360 for pie charts. A full pie chart is 360°.
- Ignoring the pictogram key. Each symbol may stand for more than one item.
- Comparing numbers across pie charts. Pie charts show proportions; the totals may differ.
- Joining the points on a scatter graph. Draw a single straight line of best fit instead.
- Saying correlation proves cause. Correlation shows a relationship, not that one causes the other.
How charts and diagrams are examined
Statistical charts make up a large share of the Foundation data questions, and scatter graphs are tested at Higher too. Questions ask you to:
- read, complete or draw bar charts and pictograms
- work out pie chart angles, or frequencies from a pie chart
- describe correlation and draw a line of best fit
- use a line of best fit to estimate, and comment on reliability
The charts and diagrams worksheet includes answers. For scatter graphs, see the scatter graphs worksheet, and use the GCSE data revision engine for more.
Charts are chosen according to the type of data. For continuous data, see histograms.
Frequently asked questions
How do you work out pie chart angles?
Divide 360° by the total, then multiply by each frequency.
What is positive correlation?
As one variable increases, the other tends to increase as well.
Why is extrapolation unreliable?
Because the trend may not continue outside the range of the data collected.