Introduction
In the world of data, often there is an interest in the number of times, or frequency, that something occurs. It could be the number of road accidents caused by drink driving, the number of hot days in a year, or the number of visits to a website in a month.
In situations like these, where the same data value can occur multiple times, the data can be organised into a frequency table.
Categorical data and frequency tables
As an example, say that the colour of every car that passed though a given intersection was recorded over a ten minute period:\text{green,\, white,\, yellow,\, white,\, black,\, green,\, black,\, blue,\, blue,\, silver,\, white,\, black,\, green,\, blue,\, blue,}\\ \text{white,\, black,\, silver,\, silver,\, red,\, red,\, red,\, black,\, white,\, blue,\, white,\, black,\, silver,\, silver,\, white,\, blue,}\\ \text{ white,\, black,\, yellow,\, blue,\, white,\, white,\, red,\, green,\, silver,\, black,\, white,\, black,\, white.}
The same colours are occurring multiple times, so it makes sense to organise the data using a frequency table.
Notice that the frequency table has three columns:
The first column shows the subgroups within the data
The tally column (optional) uses tally marks to record the frequency of each subgroup
The final column sums the tally marks and records the frequency as a number
The sum of the frequencies is equal to the total number of data values. In this case, the colours of 44 vehicles were recorded.
The graph on the right is a column graph, which will be discussed further below. Column graphs are well suited for displaying frequencies for categorical data. The table and graph allow us to analyse the frequency distribution - how the frequency of outcomes is spread across the different categories.
Examples
Example 1
Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that 15 people had no pets, 19 people had one pet, 3 people had two pets and 8 people had three pets.
Write Mr. Rodriguez's results in the frequency table below.
| Number of pets | Frequency |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 |
Frequency tables organise the same data value that occurs multiple times.
Column graphs
A column graph (or bar graph) is a graph used to display relative quantities of data in different categories. There are a wide range of topics where this type of graph can be useful.
Column graph features to remember:
Title the graph clearly
Label each axis
Label each category and give the vertical axis a clear scale
Make sure the columns are equal widths and equally spaced
Make sure that the height of the column matches the value it represents which is often the frequency of the category (how often that outcome occurred)
Examples
Example 2
Miss Yen recorded her students' favourite pets in the column graph below.
Which type of pet is most popular?
Which pet is least popular?
How many students picked a fish as their favourite pet?
How many students were surveyed in total?
Example 3
John had 7 blue marbles, 4 black marbles, 8 yellow marbles, 13 white marbles, and 6 red marbles. Use this information to complete the column graph.
Column graph features to remember:
Title the graph clearly
Label each axis
Label each category and give the vertical axis a clear scale
Make sure the columns are equal widths and equally spaced
Make sure that the height of the column matches the value it represents which is often the frequency of the category (how often that outcome occurred)