An example of quantitative data is any dataset made of numbers where arithmetic comparisons are meaningful. Typical quantitative variables represent counts (how many) or measurements (how much).
Quantitative data are observations of a numerical variable \(X\) such that differences and averages have an interpretable meaning (for example, “10 cm taller” or “2 more defects”).
Examples of quantitative data (with classification)
| Variable (example of quantitative data) | What it measures | Type | Typical units | Why it is quantitative |
|---|---|---|---|---|
| Number of emails received in a day | Count of items | Discrete | emails | Counting produces whole numbers; adding or averaging counts is meaningful. |
| Number of defective bulbs in a box | Count of defects | Discrete | bulbs | Represents how many; values jump by integers. |
| Height of a student | Physical measurement | Continuous | cm (or m) | Measured on a scale; intermediate values are possible. |
| Time to complete a task | Duration | Continuous | s, min | Time is measured; small changes are meaningful. |
| Temperature of a solution | Thermal state | Continuous | \(^\circ\!C\) or K | Measured on a numerical scale; differences represent actual changes. |
| Blood pressure (systolic) | Physiological measurement | Continuous | mmHg | Numerical measurement; averages and differences are interpretable. |
Discrete vs continuous quantitative data
- Discrete quantitative data come from counting and take separated values (often integers): \(0,1,2,\dots\).
- Continuous quantitative data come from measuring and can take any value in an interval (within measurement precision).
- If the question is “How many?” the data are typically discrete.
- If the question is “How much?” or “How long?” the data are typically continuous.
- If numbers are only labels (for example, 1 = Group A, 2 = Group B), the data are not truly quantitative; they are coded qualitative categories.
Visualization: how quantitative data often look in graphs
Mini worked example using quantitative data
Consider a small dataset of heights (in cm): \(168, 172, 170, 174, 166\). The sample mean is computed by \[ \bar{x}=\frac{168+172+170+174+166}{5}=\frac{850}{5}=170. \] The result \(\bar{x}=170\) cm is meaningful because the variable is quantitative and measured on a numerical scale.
Summary
Quantitative data are numerical observations such as height, time, temperature, and counts like the number of defects. Discrete quantitative data come from counting, and continuous quantitative data come from measuring on a scale.