STATISTICS · TEXTBOOK LESSON
Statistics is the study of collecting, organising, analysing and interpreting data. Good statistical reasoning considers both the calculations and whether the data and method are appropriate for the question.
Learning objectives
By the end of this lesson, you should be able to:
- Organise data using suitable tables and graphs.
- Calculate and interpret measures of centre and spread.
- Compare data sets using numerical and graphical evidence.
- Identify limitations such as biased samples or misleading scales.
1. Key vocabulary and definition
Definition
Mean = total of values / number of values. Median is the middle value after ordering. Mode is the most frequent value. Range = maximum - minimum.
datameanmedianmoderangedistributionsample
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- The mean uses every value and can be affected strongly by outliers.
- The median is resistant to extreme values.
- A graph can mislead if axes are truncated, intervals are inconsistent or areas are used incorrectly.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Check how the data were collected and what each variable represents.
2
Choose a suitable representation for the data type.
3
Calculate appropriate summary measures.
4
Describe patterns, spread, unusual values and relationships.
5
State conclusions cautiously and in context.
4. Worked example
Worked example
Find the mean, median and range of 3, 5, 5, 7, 10.
1
Mean = (3+5+5+7+10)/5 = 30/5 = 6.
2
The data are already ordered, so the middle value is 5; median = 5.
3
Range = 10 - 3 = 7.
4
These measures describe centre in different ways and the total spread.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Find the mean of 4, 7, 9, 10.
- Find the median of 2, 6, 8, 9, 12.
- Find the mode of 3, 4, 4, 4, 6, 8.
- Find the range of 11, 15, 19, 22.
- Give one reason a graph with a vertical axis starting at 95 instead of 0 might exaggerate differences.
Show answers
- 7.5
- 8
- 4
- 11
- It visually magnifies small differences in values
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.