Statistical Diagrams

Video coming soon3 worked examples

Theory

The Golden Rule: When constructing a pie chart, you must remember to multiply your fraction by 360 to find the angle. A very common lost mark is calculating percentages (multiplying by 100) instead of angle sizes.

1. Pie Charts

A pie chart represents data as slices of a full $360^\circ$ circle.

Constructing: Add up all the values to find the total. For each category, write the value as a fraction of the total, then multiply by $360^\circ$ to find the exact angle for the slice.
Formula: $\frac{\text{Amount}}{\text{Total}} \times 360^\circ$ .
Interpreting: If you know the angle of a slice, its fraction of the whole is simply $\frac{\text{Angle}}{360^\circ}$ .

2. Scatter Graphs & Lines of Best Fit

A scatter graph plots two different variables to see if there is a relationship (correlation) between them.

Positive correlation: As one value goes up, the other goes up (e.g., temperature and ice cream sales).
Negative correlation: As one value goes up, the other goes down (e.g., temperature and umbrella sales).
Line of Best Fit: This is a single, straight line drawn with a ruler through the middle of the plotted points. It must follow the general trend/direction of the data, with roughly an equal number of points above and below the line.
Estimating: Draw a line from the given value on one axis to your line of best fit, and then across to the other axis. Your estimate must match your specific line, even if your line is slightly different from someone else's.

3. Stem-and-Leaf Diagrams

A stem-and-leaf diagram displays quantitative data split into a "stem" (the first digits) and "leaves" (the last digit).

The data must be ordered sequentially.
A back-to-back stem-and-leaf diagram allows you to compare two different sets of data at once (e.g., ages of men vs women).
You must always include or check the Key (e.g., $3 | 0 = 30$ ) to understand what the numbers represent.

4. Compound Bar Graphs

Compound (or comparative) bar graphs allow you to compare like-for-like data side-by-side using two or more sets of bars on the same axes.

⚠️ Common Examiner Traps

The "Percentages instead of Angles" Trap: When asked to construct a pie chart, candidates frequently divide the amount by the total and multiply by 100. This calculates a percentage, not an angle! You cannot draw a 25% slice with a protractor; you must multiply by 360 to find the $90^\circ$ angle.
The "Dot-to-Dot" Trap: When asked to draw a line of best fit, candidates sometimes join all the individual points together in a zig-zag pattern using their ruler. A line of best fit must be a single, continuous, straight line that slices through the middle of the data.
The "Ignoring Your Own Line" Trap: When asked to estimate a value using your line of best fit, you must read the answer strictly from the line you drew. If you try to guess the answer mathematically without looking at your drawn line, you will lose the mark. The examiner checks if your answer perfectly matches your graph.

Worked examples

Example 1

A researcher carried out a survey to determine people's preferred type of chocolate. The results are shown below:

White: 20
Milk: 34
Dark: 26

Calculate the angles required to construct a pie chart to illustrate this information. (3 marks)

Step 1: Calculate the total number of people surveyed.

20 + 34 + 26 = 80 \text{ people}

Step 2: Calculate the angle for White Chocolate.

\frac{20}{80} \times 360^\circ = 90^\circ

Step 3: Calculate the angle for Milk Chocolate.

\frac{34}{80} \times 360^\circ = 153^\circ

Step 4: Calculate the angle for Dark Chocolate.

\frac{26}{80} \times 360^\circ = 117^\circ

(Self-Check: $90 + 153 + 117 = 360^\circ$ . The candidate would then use a protractor to accurately draw these slices).

Example 2

Harris recorded the departure time (am) and his journey time (minutes) to work.

Departure time: 7:32, 7:36, 8:10, 7:40, 8:02, 7:50, 8:04, 7:45
Journey time: 22, 21, 37, 25, 32, 28, 36, 24

Harris plots the data on a scatter graph and draws a single straight line of best fit. Tomorrow, Harris plans to depart at 7:55 am. Explain how he would use his line of best fit to estimate his journey time. (1 mark)

Step 1: Locate 7:55 am on the horizontal x-axis (Departure Time).

Step 2: Draw a straight vertical line upwards from 7:55 am until it exactly hits the drawn line of best fit.

Step 3: From that specific point on the line of best fit, draw a straight horizontal line across to the vertical y-axis to read the estimated journey time.

Example 3

A back-to-back stem-and-leaf diagram shows the number of people who went to the cinema to see an Action Film and a Comedy Film over 10 nights.

For the Comedy film, the "leaves" next to the "7" stem are: 7, 6, 5, 3.
For the Action film, the "leaves" next to the "7" stem are: 5.

The key states $8 | 4 = 48$ people for the comedy side, and $4 | 1 = 41$ people for the action side.

(a) What was the largest number of people who went to see the action film? (1 mark)

(b) What was the smallest number of people who went to see the comedy film? (1 mark)

Step 1: Interpret the stems. The "7" stem represents numbers in the 70s.

Step 2 (Action): Looking at the Action side, the highest stem with a leaf is 7, and the leaf is 5.

Answer (a): The largest number of people for the action film was 75.

Step 3 (Comedy): Looking at the Comedy side, the lowest stem with leaves is 4, and the leaves are 8.

Answer (b): The smallest number of people for the comedy film was 48.

Ready to practise?

9 Statistical Diagrams questions with answers and video solutions