A messy list of 200 exam marks tells you nothing. Tally how many fall in each 10-mark band, and suddenly you can see the whole class at once.
A frequency distribution is a table (or chart) showing how often each value — or each range of values — occurs in a dataset.
It's the bridge from raw data to a histogram, and the starting point for finding the mode, spotting skew, and computing grouped means.
Building one
- Choose classes (intervals) of equal width covering all the data.
- Tally how many values fall in each class.
- Optionally add cumulative frequency (running total).
- Optionally add relative frequency (proportion of the total).
Why use classes (10-19, 20-29...) instead of listing every individual value?
Estimate the mean from a grouped frequency table.
Use the midpoint of each class as its representative value, multiply by the frequency, sum, and divide by the total frequency. It's an estimate — the real values are hidden inside the classes.
Overlapping or unequal classes break everything. 10-20 and 20-30 — which class does 20 go in? Use clear, non-overlapping intervals like 10-19, 20-29.
5-15 classes is the usual sweet spot. Too few → detail vanishes; too many → it's barely better than the raw list.
- Counts how often each value/range occurs.
- Group into equal, non-overlapping classes for big datasets.
- Foundation for histograms, modal class, and grouped means.