Why this matters
Before you can analyse anything you have to know what kind of data you are holding. You can average people's heights, but averaging their phone numbers is nonsense. Picking the right chart, the right statistic, and the right conclusion all start with the type of data.
The idea
Data splits into two families.
Quantitative data is numbers whose size means something, so you can add them and compare how big they are. It comes in two scales:
- Interval scale: the gaps between numbers are equal and meaningful, but the zero is just a chosen reference, so ratios make no sense. Temperature and calendar years are interval, and 20 °C is not "twice as hot" as 10 °C.
- Ratio scale: there is a true zero, so both gaps and ratios mean something. Length, weight and age are ratio, and 10 kg really is twice 5 kg.
Qualitative data uses numbers or labels to tell categories apart, not to measure an amount:
- Nominal scale: labels only name a group, with no order. Think blood type, phone number, or the name of a state.
- Ordinal scale: the order matters but the gaps do not, like a test ranking or a school grade level. 1st and 2nd are in order, but the gap between them is not a fixed amount.
Once data is collected, analysis itself comes in two approaches. Descriptive statistics summarizes the data in hand (mean, median, spread). Inferential statistics uses a sample to draw conclusions about a larger population (hypothesis testing, confidence intervals).
Picture it
flowchart TD
A[A piece of data] --> B{Is its number size meaningful?}
B -- Yes --> Q[Quantitative]
B -- No --> L[Qualitative]
Q --> Q1{True zero, ratios meaningful?}
Q1 -- Yes --> RA[Ratio scale: length, weight]
Q1 -- No --> IN[Interval scale: temperature, year]
L --> L1{Does order matter?}
L1 -- Yes --> OR[Ordinal scale: ranking, grade]
L1 -- No --> NO[Nominal scale: blood type, phone number]Worked example
Classify "test ranking". It is not an amount (2nd place is not "two of something"), so it is qualitative. But the order clearly matters: 1st beats 2nd beats 3rd. The gaps are not fixed (1st to 2nd may be a landslide while 2nd to 3rd is a tie). Order yes, gaps no, so it is the ordinal scale. Compare "weight": it is a number whose size means something, and 0 kg is a true zero, so it is quantitative, ratio scale.
Your turn
Practise sorting examples into quantitative versus qualitative, and matching values to interval, ratio, nominal, or ordinal scales.
Recap
- Quantitative = numbers whose size matters; qualitative = labels for categories.
- Quantitative splits into interval (meaningful gaps, no true zero) and ratio (true zero, ratios work).
- Qualitative splits into nominal (no order) and ordinal (order but uneven gaps).
- Descriptive statistics summarize a sample; inferential statistics generalize to a population.