What is a Frequency Distribution?

A frequency distribution is a full way of classifying the raw data of a quantitative variable. It shows how the different values of the variable are spread across several classes, together with each class's frequency. For the mathematics marks there are ten classes: 0–10, 10–20, …, 90–100.

Key terms:

• Class frequency — the number of observations falling in a class. In the class 30–40 there are 7 raw values (30, 37, 34, 30, 35, 39, 32), so its frequency is 7. (A value of exactly 40 is not counted here — it goes into 40–50 — for a reason explained under class limits.)
• Class limits — the two ends of a class: the smaller is the lower class limit, the larger the upper class limit. For 60–70 the lower limit is 60 and the upper limit is 70.
• Class interval (class width) — the gap between the two limits: $\text{class interval} = \text{upper limit} - \text{lower limit}$. For 60–70 it is $70-60=10$.
• Class mid-point (class mark) — the middle value of a class:

Once data are grouped, individual values are dropped and the class mark represents the whole class in later calculations. For the mark classes:

A frequency curve is the graphic form of a frequency distribution — class marks on the X-axis, frequencies on the Y-axis, the plotted points joined into a curve.