Frequency table

Before computing any index, the first step in organising a set of data is to collect them in a frequency table, which counts how many times each value appears.

Definition — Frequency table

Given a sample of $n$ observations taking values (or classes) $v_1,\ldots,v_k$:

• absolute frequency $f_i$: number of observations equal to $v_i$;
• relative frequency $h_i=f_i/n$ (always in $[0,1]$);
• percentage frequency $h_i\cdot 100\%$;
• cumulative frequency $F_i=\sum_{j\le i} f_j$.

One always checks: $\sum_i f_i=n$ and $\sum_i h_i=1$.

The cumulative frequency is useful for answering questions of the type “how many observations are at most $v_i$?”: it is read directly off the last column.

Example — Test marks in a table

On a test taken by $10$ pupils the marks are $4,5,6,6,7,7,7,8,9,10$:

mark	$f$	$h=f/10$	$F$ cumulative
$4$	$1$	$0,10$	$1$
$5$	$1$	$0,10$	$2$
$6$	$2$	$0,20$	$4$
$7$	$3$	$0,30$	$7$
$8$	$1$	$0,10$	$8$
$9$	$1$	$0,10$	$9$
$10$	$1$	$0,10$	$10$
total	$10$	$1,00$	—

Links

Topics: Probabilita
Concepts: Frequenza cumulata · Frequenza relativa · Tabella di frequenza
Methods: Tabella frequenza
Skills: Calcolare · Interpretare grafico