1 Types of Data
| Type | Description | Examples |
|---|---|---|
| Qualitative (categorical) | Describes a category or quality — not a number | Eye colour, favourite sport, gender |
| Quantitative (numerical) | Expressed as a number — can be measured or counted | Height, temperature, number of siblings |
| Discrete | Countable, specific values only | Number of students: 0, 1, 2, 3 … |
| Continuous | Can take any value in a range (measured) | Height: 162.3 cm, time: 4.72 s |
🔑Ask: "Can I measure it with a ruler/scale/stopwatch?" → likely continuous. "Can I only count it?" → discrete.
Population vs Sample
- Population: every individual in the group of interest
- Sample: a smaller group selected from the population to represent it
- A good sample is random and representative — no bias
2 Organising Data
Frequency Table
Lists each value and how many times it occurs (frequency). A relative frequency table shows the fraction or percent of the total.
| Score | Frequency (f) | Relative frequency |
|---|---|---|
| 60 | 3 | 3/20 = 15% |
| 70 | 7 | 7/20 = 35% |
| 80 | 6 | 6/20 = 30% |
| 90 | 4 | 4/20 = 20% |
| Total | 20 | 100% |
Stem-and-Leaf Plot
Displays data in order. The stem is the leading digit(s); the leaf is the last digit.
✏️
Data: 23, 25, 31, 34, 38, 42
2 | 3 5
3 | 1 4 8
4 | 2
2 | 3 5
3 | 1 4 8
4 | 2
3 Measures of Central Tendency
Mean (average)
mean = sum of all values / number of values
Median
middle value when data is sorted in order
Mode
value that appears most often
Finding the Median
- Odd number of values: middle value. E.g. {2, 5, 7, 9, 12} → median = 7
- Even number of values: average of the two middle values. E.g. {2, 5, 7, 9} → median = (5+7)/2 = 6
✏️
Data: 4, 8, 6, 5, 3, 9, 6
Sorted: 3, 4, 5, 6, 6, 8, 9 (7 values)
Mean = (3+4+5+6+6+8+9)/7 = 41/7 ≈ 5.86
Median = 4th value = 6
Mode = 6 (appears twice)
Sorted: 3, 4, 5, 6, 6, 8, 9 (7 values)
Mean = (3+4+5+6+6+8+9)/7 = 41/7 ≈ 5.86
Median = 4th value = 6
Mode = 6 (appears twice)
Choosing the Right Measure
| Measure | Best used when | Weakness |
|---|---|---|
| Mean | Data is symmetric with no outliers | Affected by extreme values (outliers) |
| Median | Data has outliers or is skewed | Ignores most of the data |
| Mode | Data is categorical, or you want most common | May not exist, or multiple modes |
4 Measures of Spread
Range
range = maximum − minimum
The range shows how spread out the data is. A large range means data is more variable.
💡Two data sets can have the same mean but very different spreads. Always report both central tendency and spread for a complete picture.
5 Graphs
| Graph type | Best for | Key feature |
|---|---|---|
| Bar graph | Comparing categories (qualitative or discrete data) | Bars do not touch; height = frequency |
| Histogram | Continuous data grouped in intervals | Bars touch; no gaps between them |
| Line graph | Data over time (showing trends) | Points connected by lines |
| Circle/pie chart | Parts of a whole (relative frequencies) | Sector angle = (freq/total) × 360° |
| Stem-and-leaf | Showing distribution of small data sets | Preserves original values |
Sector Angles for Pie Charts
Sector angle
angle = (frequency / total) × 360°
✏️30 students surveyed. 12 chose hockey. Sector angle = (12/30) × 360° = 144°
6 Common Mistakes to Avoid
| Mistake | What to do instead |
|---|---|
| Not sorting data before finding median | Always sort the data in ascending order first. |
| Using mean when there are outliers | An outlier skews the mean. Use median for data with extreme values. |
| Confusing bar graph and histogram | Bar graph: gaps between bars (categorical). Histogram: no gaps (continuous/grouped). |
| Forgetting to check total frequency | All frequencies in a table must sum to the total number of data points. |
| Sector angle adding up wrong | All sector angles must sum to exactly 360°. |
| Confusing discrete and continuous | Discrete = counted (whole numbers). Continuous = measured (any value). This determines the correct graph type. |