Frequency distribution

Ungrouped frequency tables

A frequency distribution table is useful for organising and collating data. It shows (in the frequency column, obten denoted by the letter f) how many times a piece of data (score) has occurred in a set of information.

The number of days absence during a term of a group of 30 students at a sixth form college is:

 2 3 0 1 5 1 0 3 3 2 5 3 2 0 3 3 2 1 1 0 2 1 0 3 4 4 2 1 0 3

Summarised in a ungrouped frequency table:

 Number of days absence 0 1 2 3 4 5 Frequency 6 6 6 8 2 2

In a frequency table, the left-hand column shows the value of the variable. The right-hand column shows the frequency with which each individual value of the variable occurs.

It is advisible to total the frequency column to ensure that none of the data was missed from the count, or that none has been counted twice. The total of this column, , must always come to the number of observations, n, in the data set.

Cumulative frequency tables

Another column can be added to a frequency distribution table: a cumulative frequency column. This shows progressive totals of the scores. The cummulative frequency of a given score is the number of scores lessthan or equal to that score.

Draw a cummulative frequency distribution table for this data:

1 2 3 2 1 0 4 3 3 2
0 2 2 1 4 2 3 1 2 0
1 1 3 2 0 2 4 4 1 0

The cummulative frequency table is:

 Score Frequency (f) Cummulative frequency (cf) 0 5 5 1 7 12 2 9 21 3 5 26 4 4 30 =30

Frequency distribution table for qualitative data

A frequency distribution table (or frequency table) for qualitative data lists all the categories and the number of elements in the data set that belongs to each category. The number of elements in a category is called the frequency of that category which displays the number of times the category occurs in a collection of data.