What is Count and frequency? — Mathematics

Definition 50.1 Primary & Middle School Mathematics · Chapter 50 — Organizing Data

For each possible value of a survey, its count is the number of times it appears; its frequency is the count divided by the total number of observations:

\text{frequency} = \frac{\text{count}}{\text{total}} .

Frequencies can be written as fractions, decimals or percentages, and they always add up to $1$ (i.e. $100\,\%$ ).

Examples

Example 50.2

Favorite sport of the $25$ students of a class, from the raw list to the table:

sport	football	swimming	tennis	judo	total
count	$10$	$6$	$5$	$4$	$25$
frequency	$0.40$	$0.24$	$0.20$	$0.16$	$1$

For football: $\frac{10}{25} = \frac{40}{100} = 0.40 = 40\,\%$ . The frequency row must sum to $1$ — a permanent, free check.

Example 50.4 (Classes)

The heights (in cm) of $20$ students range from $148$ to $172$ . Listing every height separately would give a table with almost as many columns as students; instead, group into classes:

height (cm)	$\intco{145}{155}$	$\intco{155}{165}$	$\intco{165}{175}$	total
count	$5$	$9$	$6$	$20$
frequency	$0.25$	$0.45$	$0.30$	$1$

Each height is counted in exactly one class ( $155$ goes in $\intco{155}{165}$ , not in both — that is why the intervals are half-open). Grouping loses detail but gains readability.

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Examples

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