Statistical charts and diagrams.
Turn frequencies into clear bar charts, pie charts and pictograms, and read their scales accurately.
Use simple, dual and composite bar charts · calculate sector angles · interpret pictogram keys and frequency tables
Choose and label a bar chart
A bar chart turns category frequencies into heights on a shared scale. A taller bar means more observations in that category, so equal scales and clear category labels are essential.
A dual chart puts two groups side by side for each category. A composite chart stacks their contributions to show both a total and its parts. Read each group through the key, and distinguish a stacked segment’s thickness from its top coordinate.
Bar charts compare categories or discrete values. Use a title, labelled axes, a consistent scale and equal-width bars. A key distinguishes multiple groups.
Each club has two separate bars. Compare the year groups using the same vertical scale.
In the composite chart, Art has total 13 and its Year 10 segment is 8. Find the Year 11 frequency.
Read the thickness of a stacked segment, not just its top coordinate.
Pause and explainIn a stacked bar, why subtract the lower height from the upper height for the top group?
The upper coordinate includes the groups below it. The difference isolates the thickness belonging to the top group.
Convert frequencies into pie-chart angles
A pie chart shows how a whole is divided into proportions. The full circle is one whole, so it corresponds to all observations and to 360°.
A category’s fraction of the observations must occupy the same fraction of the full turn. Find frequency divided by total, then multiply by 360°. To reverse the process, use the sector’s fraction of 360° to find the corresponding share of the total population.
8 of 20 students choose Art. Find its sector angle.
A sector is 72° in a survey of 150 people. Find its frequency.
Pause and explainIf a category contains half the observations, what angle should its sector have?
180°, half of the full 360° circle.
Read every symbol using the pictogram key
A pictogram replaces a number of observations with a repeated symbol. The key tells us how much each whole symbol represents; its picture has no numerical meaning without that key.
Count whole symbols and permitted fractions of symbols separately, then multiply by the represented quantity. A half symbol means half of the key amount, not necessarily one object. Keep symbols the same size so their frequency is conveyed by repetition rather than changing area.
Key: ● represents 2 students; ◐ represents 1 student.
A row shows three whole symbols and one half symbol. The key is one whole symbol = 2 students. Find the frequency.
Keep symbols the same size. If a whole symbol represents 4 objects, a half symbol represents 2, not 12 an object.
Pause and explainIf one whole symbol represents 8 people, how many does a half symbol represent?
4 people, half of the key amount.
Build a simple frequency distribution
A simple frequency distribution records how often each value occurs. It is useful for both counting observations and summarising numerical quantities, but those calculations answer different questions.
Adding frequencies counts individuals. Multiplying each value by its frequency and adding counts the total measured quantity. For example, students owning three pets contribute one student each but three pets each. Decide which total the question requests before calculating.
| Pets | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Frequency | 3 | 5 | 3 | 1 |
How many students own at least two pets? How many pets are owned in total?
Students with at least two pets: 3 + 1 = 4 students.
Total pets: 0 × 3 + 1 × 5 + 2 × 3 + 3 × 1 = 14 pets. Frequencies count students, while the weighted sum counts their pets.
Pause and explainIf 4 students each own 2 pets, what are the student count and pet count?
There are 4 students and 8 pets. Frequency counts students; value times frequency counts their pets.
Your turn. Use the scale or key.
Read the title, units, scale and key before extracting a value. For pie charts, identify the whole population corresponding to 360°.
Show the conversion between frequencies, angles or symbols. For composite bars, use segment thickness, and for frequency tables distinguish a count of individuals from a total of the measured values.
A pie chart represents 80 people. A category has frequency 18. Find its angle.
Reveal worked answer
A 120° sector represents 24 people. Find the total number represented.
Reveal worked answer
A pictogram key is one whole symbol = 6 cars. A row has 212 symbols. Find the number of cars.
Reveal worked answer
A stacked bar reaches 19. Its lower segment reaches 11. Find the upper segment frequency.
Reveal worked answer
For the pets table, find the proportion of students who own no pets.