We are often interested 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 example
The colour of every car that passed though a given intersection was recorded over a ten minute period:
green, white, yellow, white, black, green, black, blue, blue, silver, white, black, green, blue, blue, white, black, silver, silver, red, red, red, black, white, blue, white, black, silver, silver, white, blue, white, black, yellow, blue, white, white, red, green, silver, black, white, black, white.
We can see that the same colours are occurring multiple times, so it makes sense to organise the data using a frequency table.
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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$44 vehicles were recorded.
The graph on the right is a column graph. Column graphs are well suited for displaying frequency data for both categorical and discrete numerical data. The table and graph allow us to analyse the frequency distribution - how the frequency of outcomes is spread across the different categories.
Use the following applet to create your own column graph for the data:
For creating column graphs:
- 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) or relative frequency (the percentage of how often that outcome occurred)
Numerical data example
When displaying discrete numerical data we still use column graphs to display frequency distributions. For continuous numerical data we will use a similar graph called a histogram. We will look in more detail at histograms in our next lesson. Below are some examples and a brief description of their differences.
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Practice questions
Question 1
Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that $15$15 people had no pets, $19$19 people had one pet, $3$3 people had two pets and $8$8 people had three pets.
Write Mr. Rodriguez's results in the frequency table below.
Number of Pets Frequency $0$0 $\editable{}$ $1$1 $\editable{}$ $2$2 $\editable{}$ $3$3 $\editable{}$
Question 2
In a survey, $20$20 people were asked how many languages they spoke. Here are their answers:
$1,1,1,2,3,2,3,1,1,1,2,2,1,1,1,3,1,1,1,1$1,1,1,2,3,2,3,1,1,1,2,2,1,1,1,3,1,1,1,1
Count how many people said $1$1, $2$2 or $3$3 languages and record the results in the table.
Number of Languages Number of People 1 $\editable{}$ 2 $\editable{}$ 3 $\editable{}$ Draw a column graph to show the information in the table.
Question 3
Use the given column graph to complete the frequency table.
Score $(x)$(x) Frequency $(f)$(f) $1-5$1−5 $\editable{}$ $6-10$6−10 $\editable{}$ $11-15$11−15 $\editable{}$ $16-20$16−20 $\editable{}$ $21-25$21−25 $\editable{}$ $26-30$26−30 $\editable{}$ $31-35$31−35 $\editable{}$