Tallying and frequency charts (including tally charts for grouped data) - KS3 Maths

Key points

An image of a tally chart. — Image caption,
Tally marks and frequency tables can make it easier to sort and calculate data.

Frequency charts show the of data using marks, called tallies.
Tallying is a way of recording data that counts in groups of five. The data is tallied as it is counted, with a mark for each piece of data, and then the frequency is recorded at the end.
Tally charts can be used for grouped and ungrouped data:
- Ungrouped data is data given as separate pieces. It is useful when there is a small number of .
- Grouped data is used when there are large numbers of possible outcomes. It makes the data easier to read.

How to use ungrouped frequency charts

Ungrouped data is data that is displayed exactly how it was gathered. It has a small number of outcomes which are .
Frequency charts show the tally next to each outcome, along with the frequency of the tally.
From the frequency chart, it is easy to read the and the spread of the data.

Example

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Image caption,
This is the data gathered from a survey about the colours of cars in a car park. This data can be displayed in a frequency chart.
Image caption,
The colours of cars go in the left-hand column. The tally will go in the middle column, and the frequency can be added in once all the car colours are counted.
Image caption,
To start, the cars from the first row can be added to the chart.
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Once a tally gets to five, a new one is started next to it. A tally of five is represented in the blue row, as there have been five blue cars so far.
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Continue until all the cars have been counted and marked in the tally column.
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The tallies can now be added up to make the frequency. Tallies are useful as it is very clear to see a count of five, so this can make adding up quicker.

Question

The chart below shows the results of a survey where people were asked which type of drink they preferred.

How many people preferred lemonade?

An image of a table with two columns and five rows. The first column is labelled, drink, and is populated with the drinks, orange juice, tea, lemonade, other. The second column is labelled, tally. There are eight tally marks in the cell to the right of orange juice; drawn as a set of five and three single tally marks. There are fourteen tally marks in the cell to the right of tea; drawn as two sets of five and four single tally marks. There are thirteen tally marks in the cell to the right of lemonade; drawn as two sets of five and three single tally marks. There are four tally marks in the cell to the right of other; drawn as four single tally marks. The cells for the labels are coloured purple.

How to use grouped frequency charts

When there is a larger number of possible outcomes, it is often easier to group the data.
To group data, first decide on appropriate based on the range of likely possible answers.
For example, in a survey about the number of magazines bought by students over the space of a year, the answers given range from 0 to 100. It would be sensible to group the data in class intervals of 5, so 0–4, 5–9, 10–14, 15–19 and so on.
When grouping data, it is important not to have an overlap of values in the class intervals. 0–5 and 5–10 would not be sensible groups as there is an overlap and 5 belongs in two class intervals.
Once finished, the table is known as a grouped frequency chart.

Example

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Image caption,
Here is the data from a survey asking people how many times they bought a certain brand of yogurt in a month. There is a wide range of answers so it would make sense to group this data before making a frequency chart.
Image caption,
The answers range from 0 to 34. A sensible grouping would be to put the data into groups of 5, as shown here. It is important to make sure no class intervals overlap.
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The data can be counted into the table using tallies. Each piece of data is put into the correct class interval, so 14 is counted in the 10–14 class interval.
Image caption,
To complete the grouped frequency chart, the tallies can be added up and the frequency for each column written in.

Question

The chart below shows the results of a survey where people were asked how long it takes them to walk to school.

How many people took more than 11 minutes?

An image of a table with two columns and seven rows. The first column is labelled, journey length, measured in minutes, and is populated with the groups, zero to three, four to seven, eight to eleven, twelve to fifteen, sixteen to nineteen, and more than twenty. The second column is labelled, tally. There are two tally marks in the cell to the right of zero to three; drawn as two single tally marks. There are eight tally marks in the cell to the right of four to seven; drawn as a set of five and three single tally marks. There are four tally marks in the cell to the right of eight to eleven; drawn as four single tally marks. There are twelve tally marks in the cell to the right of twelve to fifteen; drawn as two sets of five and two single tally marks. There are two tally marks in the cell to the right of sixteen to nineteen; drawn as two single tally marks. There are three tally marks in the cell to the right of more than nineteen; drawn as three single tally marks. The cells for the labels are coloured purple.

Practise working with tallying and frequency charts

Practise working with tallying and frequency charts with this quiz. You may need a pen and paper to help you with your answers.

Quiz

Real-life maths

Tally marks are written differently all around the world.

In some countries, such as Brazil and France, tallies are represented like this:

A series of five images. Each image shows a representation of the numbers one to five in a tally. The first image is a single vertical line. The second image is two lines, forming two edges of a square; the left and top edges. The third image is three lines, forming three edges of a square; the left, top, and right edges. The fourth image is four lines, forming a square. The fifth image is five lines; four lines forming a square and a diagonal joining the bottom left and top right corners.

In other places, such as China and Hong Kong, it is more common to see tallies that look like this:

A series of five images. Each image shows a Chinese character to represent the numbers one to five in a tally.

The common feature of all the different styles of tally marks is that after five marks have been recorded, another set starts. This is because counting used to be done more commonly using hands. With only four fingers and one thumb on one hand, anyone counting must start again after reaching a count of five.