DATA TYPES
Qualitative
categories, not numbers
Quantitative
numerical (counted/measured)
Discrete
countable (0, 1, 2, 3 …)
Continuous
measured (any value, e.g. 1.73 m)
Discrete → bar graph
Continuous → histogram
POPULATION & SAMPLE
Population
entire group of interest
Sample
subset used to represent it
- Good sample = random & representative
- Biased sample → unreliable conclusions
RANGE
MEASURES OF CENTRAL TENDENCY
Mean ★
sum of values ÷ count
Median
middle value when sorted
MEDIAN — HOW TO FIND
- Sort data in ascending order first
- Odd count: middle value
- Even count: mean of 2 middle values
Data: 3, 4, 5, 6, 6, 8, 9 (7 values)
Mean = 41/7 ≈ 5.86
Median = 4th value = 6
Mode = 6
WHICH MEASURE TO USE?
Mean
symmetric data, no outliers
Median
skewed data or outliers present
Mode
categorical data or most popular
GRAPH TYPES
| Graph | Best for |
|---|
| Bar graph | Comparing categories (gaps between bars) |
| Histogram | Continuous data in intervals (no gaps) |
| Line graph | Change over time (trends) |
| Pie chart | Parts of a whole (%) |
| Stem & leaf | Small data sets, shows distribution |
PIE CHART — SECTOR ANGLE
Formula
angle = (f / total) × 360°
12 out of 30 chose hockey:
(12/30) × 360° = 144°
FREQUENCY TABLE
Rel. freq.
freq / total × 100%
- All frequencies must sum to total n
- Relative frequencies sum to 100%
STEM-AND-LEAF
Data: 23, 25, 31, 34, 38, 42
2 | 3 5
3 | 1 4 8
4 | 2
Stem = tens digit, leaf = units
COMMON MISTAKES
- Always sort before finding median!
- Mean ≠ reliable with outliers → use median
- Bar: gaps between bars (categorical)
- Histogram: no gaps (continuous)
- Sector angles must sum to 360°
- Frequencies must sum to total n
OUTLIER EFFECT ON MEAN
Data: 2, 3, 4, 5, 50
Mean = 64/5 = 12.8 (far from most data)
Median = 4 (better centre here)