POP

C9.1 Classifying and Tabulating Statistical Data

Image · 914 × 270

01 — Explanation

How is data classified?

Categorical (qualitative) data — non-numerical labels, e.g. favourite colour, mode of transport, eye colour.
Discrete data — numerical data taking only exact, separate values, usually whole-number counts, e.g. number of siblings, shoe size, goals scored in a match.
Continuous data — numerical data that can take any value on a scale, limited only by how precisely it's measured, e.g. height, time, mass, temperature.

The key test for discrete versus continuous is whether in-between values are physically possible: you can't score $2.5$ goals, so goals scored is discrete, but a person's height could genuinely be $162.3\text{ cm}$ or any value even more precise, so height is continuous.

02 — Explanation

How do I use a tally table?

A tally table records raw data as it's collected, using tally marks grouped in fives (with the fifth stroke crossing the previous four), before totalling into a frequency column.

Common mistake

losing track of groups of five when marks are drawn close together. Always group in fives with a diagonal fifth stroke and add up group-by-group, not stroke-by-stroke — counting each row's groups of five separately before summing is far less error-prone than counting every single mark individually.

03 — Explanation

How do I read a two-way table?

A two-way table organises data across two categories at once, with row and column totals:

	Likes Football	Dislikes Football	Row Total
Boys	18	4	22
Girls	11	9	20
Column Total	29	13	42

Worked example. Find the number of girls who dislike football, and state what fraction of all 42 students that represents.

Reading the "Girls" row and "Dislikes Football" column gives $9$ . As a fraction of the total: $\dfrac{9}{42} = \dfrac{3}{14}$ .

Exam tip

trace the exact row label and exact column label carefully — misaligning by one row or column in a busy table is an easy way to lose an otherwise simple mark.

04 — Explanation

How do I fill in a missing value in a two-way table?

Every row and column total must be internally consistent, so a missing cell can always be found using the totals that surround it, working from the values you do know towards the one you don't.

Worked example. In a two-way table, the "Boys" row totals $22$ , with $18$ boys liking football. The overall total is $42$ students, and $29$ students in total like football. Find how many girls like football, and how many girls dislike football.

Students who like football overall: $29$ . Boys who like football: $18$ . So girls who like football: $29-18=11$ . Total girls: $42-22=20$ . Girls who dislike football: $20-11=9$ .

Exam tip

work outwards from the numbers already given rather than guessing which cell to fill first — each row and column total acts as a check, so filling cells in the wrong order can mean redoing several steps if an early guess turns out to be inconsistent with a later total.