# Frequency Distributions

## Frequency

The frequency of an event is how often it occurs.

### Example

Alice the cow is up to her dare-devil circus tricks again. This time she's learning to jump of a really high platform, with the hope of landing in an inflatable kiddy-pool. As you can imagine, she doesn't manage to land in the pool every often.

She lands in the pool

• Twice on Monday
• Once on Tuesday
• Three times on Wednesday and
• Five times on Thursday
So, her frequency of landing in the pool is 2 on Monday, 1 on Tuesday, 3 on Wednesday and 5 on Thursday.

## Frequency Distribution Table

We can count how many times each score occurs in a list of data and collect them together in a frequency distribution table.

### Example

Here is a list of how many times Alice has landed in the wading pool over the past fortnight:

1,2,4,2,1,4,5,6,7,5,6,7,2,7,7
It's easier to work out how many times each number of landings occurs if we put the numbers in order:
1,1,2,2,2,4,4,5,5,6,6,7,7,7,7
Then we can count up the number (frequency) of times each number of landings occurs and put the results in a frequency distribution table:
Number of Landings Frequency
1 2
2 3
4 2
5 2
6 2
7 4

We can use this table to determine all sorts of interesting things about our data. For example,

• The most common number of landings made by Alice was 7
• She achieved most numbers of landings twice.

A frequency distribution table lists all the possible values that occur in a data set and how many times they occur (their frequencies).

### Example

Sam's maths teacher gives his class a weekly pre-test to see how well they understand the background material required for the next topic. Here are Sam's marks on the tests for the first 12 weeks of the year:

17,14,17,16,18,20,17,16,20,17,12,18
Sam's marks can be placed in a frequency table as follows
Test Mark Frequency
12 1
13 0
14 1
15 0
16 2
17 4
18 2
19 0
20 2

We can also group Sam's marks into different ranges. In the table below, each range is a group of 3 marks. The frequency is the sum of the frequencies for the marks in each range.

Mark Range Frequency
12-14 2
15-17 6
18-20 4

You can read more about grouping values in frequency distribution tables in the article on grouped frequency distributions.

## Graphing Data

Creating a frequency distribution table is a good first step in displaying your data graphically. Once your data is tabulated, you can choose to display it using a number of different methods including pie charts, bar charts and line graphs. You can read more about these methods in the article on displaying your data.

### Description

• Histograms
• Scatter plots
• Stem and leaf plots etc

these lessons are for students studying maths in Year 10 or highter

### Audience

Year 10 students or higher, however, suitable for Year 8+ students too.

### Learning Objectives

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