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Statistics is about collecting data, displaying it clearly, and drawing conclusions from it. In Key Stage 2 you work with bar charts, line graphs, pie charts, and tables — and learn how to calculate the mean average.
Discrete data can only take specific values, usually whole numbers (you cannot have 2.7 children).
Continuous data can take any value within a range.
Choosing the right type of chart depends on the type of data you have.
A frequency table records how often each value occurs.
Example — Goals scored per match:
| Goals | Tally | Frequency |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
Total matches: 4 + 7 + 8 + 3 + 2 = 24 Most common (modal) number of goals: 2 (highest frequency)
A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items — always check the key.
Example — Favourite fruit of 40 children:
| Fruit | Symbols (each = 4 children) |
|---|---|
| Apple | * * * * |
| Banana | * * * |
| Grape | * * * * * |
| Orange | * * |
Half symbols: If a symbol is shown as a half, it represents half the key value. If the key = 4, a half symbol = 2.
Reading a pictogram:
Drawing a pictogram:
A bar chart uses rectangular bars to compare categories or values. The height (or length) of each bar shows the frequency.
Reading a bar chart:
Grouped bar charts compare two or more sets of data on the same chart, using different coloured bars side by side.
Questions you can answer from a bar chart:
A line graph shows how a value changes over time. Points are plotted and joined with straight lines.
When to use a line graph: for continuous data measured at regular time intervals — temperature over a day, height over months, distance over time.
Reading a line graph:
Example: A line graph shows temperature from 6 am to 6 pm. At 6 am it is 8 degrees; at noon it is 18 degrees; at 6 pm it is 14 degrees.
A pie chart is a circle divided into sectors (slices). Each slice represents a proportion of the whole.
The full circle = 360 degrees = 100% = the total of all data.
Reading a pie chart:
Drawing a pie chart:
Example: 30 people are asked their favourite season. Summer: 12, Winter: 6, Spring: 8, Autumn: 4.
The mean is what most people mean when they say "average". To find the mean:
Example: Test scores: 7, 9, 6, 8, 10, 4
Working backwards: if you know the mean and the number of values, you can find a missing value.
Example: 5 values have a mean of 8. Four of them are 6, 9, 10, 7. What is the fifth?
Different types of data suit different charts. Use this decision tree to pick the best display:
flowchart TD
A[What kind of data?] --> B{"Categories<br/>or values over time?"}
B -->|Categories| C{"Compare sizes<br/>or show proportions?"}
B -->|Values over time| D[Line graph]
C -->|Compare sizes| E[Bar chart]
C -->|Show proportions of a whole| F[Pie chart]
A --> G{"Small data set<br/>with simple counts?"}
G -->|Yes| H["Pictogram or<br/>frequency table"]
You can use statistics to compare two sets of data. Useful comparisons:
Example: Two groups each take a test (out of 10):
Use this data about hours of sunshine per day in a week: 4, 7, 5, 8, 6, 5, 3.
Mr Khan's Year 6 class collected this data on pets owned by 30 children. The frequencies were: dogs 9, cats 8, fish 6, rabbits 4, none 3.
Step 1 — Check the total. Add the frequencies: 9 + 8 + 6 + 4 + 3 = 30. This matches the class size, so no entries are missing.
Step 2 — Find the modal category. The largest frequency is 9 (dogs). The mode is therefore dogs — that is the most popular pet. The mode is for the category name, not the frequency value.
Step 3 — Calculate proportions for a pie chart. Each child contributes an angle of 360 / 30 = 12 degrees. Multiply each frequency by 12:
Check the total: 108 + 96 + 72 + 48 + 36 = 360 degrees. Correct.
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