Introduction
Measures of central tendency (mean, median, mode) locate the "centre" of a data set, while measures of variation (range, interquartile range, standard deviation) describe how spread out the data is. In 9709 PS1, you are expected not only to calculate these measures from raw or grouped data, but also to work efficiently from coded or pre-summarised totals, and to use them to compare two data sets. Questions on this subtopic appear in almost every PS1 paper — often carrying 6–10 marks — and comparing two distributions is a common final part.
Core Concept
Measures of Central Tendency
| Measure | Description | Best used when |
|---|---|---|
| Mean | Arithmetic average; uses all data values | Data is roughly symmetric; no extreme outliers |
| Median | Middle value when ordered; splits distribution 50/50 | Data is skewed or has outliers |
| Mode | Most frequently occurring value (or modal class) | Identifying the most common category |
Measures of Variation
| Measure | Description | Advantage |
|---|---|---|
| Range | Largest − Smallest | Simple; but very sensitive to outliers |
| Interquartile range (IQR) | Robust to outliers | |
| Standard deviation | Root-mean-square deviation from the mean | Uses every data point; most powerful measure |
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