Tally Charts and Frequency Tables

Why we collect data

Imagine your class wants to know which fruit is the most popular. You could try to remember everyone's answer in your head, but that gets muddled fast. Instead, we collect data in an organised way. Two of the simplest tools are the tally chart and the frequency table.

What is a tally mark?

A tally mark is one small upright line. Each line means one.

The clever bit is how we group them. When you reach five, you draw the fifth mark across the first four, like a little gate:

||||̸ means 5.

Grouping in fives means you never have to count a long row of single lines. You just count the groups of five and add the leftovers.

Tally	Number
				3
				̸	5
				̸			7
				̸				̸	10
				̸				̸				13

Building a tally chart

Suppose 12 children each name their favourite fruit. As each child answers, you add one mark next to that fruit. Here is the chart after everyone has spoken:

Fruit	Tally
Apple					̸
Banana
Grapes
Orange

Notice you do not count at the end and try to remember. You count as you go, one mark per answer. That is what makes a tally chart so reliable.

Turning it into a frequency table

A frequency table writes the count as a number. The word frequency just means how many times. We can add a frequency column next to the tally:

Fruit	Tally	Frequency
Apple					̸	5
Banana					3
Grapes				2
Orange				2
Total		12

Tally chart vs frequency table: what is the difference?

People often use the two names for the same table, but they do different jobs.

	Tally chart	Frequency table
What it holds	Tally marks, one per item	A number for each group
When you use it	While you are collecting data	After you have finished counting
Best for	Keeping count without losing your place	Reading, comparing and drawing charts
Example row	Popcorn  |||| ||	Popcorn  7

In practice you build both at once: the tally column records the data as it arrives, and the frequency column is what you get when you count each group of marks. Most printed tables show the two side by side.

How to calculate frequency from tally marks

Because tallies are grouped in fives, you never have to count marks one at a time:

1. Count the gates — the groups of five with a line struck through them.
2. Multiply that number by 5.
3. Add the leftover single marks.

So |||| |||| ||| is two gates and three singles: 2 × 5 = 10, then 10 + 3 = 13.

Two checks worth doing every time. First, the frequencies must add up to the number of people or items you surveyed — if you asked 30 children, the column must total 30. Second, if someone adds an extra tally after you have finished, only that one row changes: add 1 to that frequency and 1 to the total, and leave every other row alone.

Worked example: reading the table

Use the fruit table above to answer questions.

• Which fruit is most popular? Look for the biggest frequency. Apple has 5, the highest, so apple wins.
• How many children chose grapes or orange? 2 + 2 = 4 children.
• How many children were surveyed? Read the Total row: 12.

Always add the frequencies to check the total. Here 5 + 3 + 2 + 2 = 12, which matches the 12 children. If it did not match, you would know a mark was missed or counted twice.

Activity: a class survey

Try this with your friends or family.

1. Pick a question with a few clear choices, such as "What is your favourite pet: cat, dog, fish or rabbit?"
2. Draw a table with a row for each choice.
3. Ask each person and add one tally mark for their answer.
4. Count each row and write the frequency.
5. Add a Total row and check it equals the number of people you asked.

Why this matters

Tally charts and frequency tables are the first step in handling data. Once your data is neatly counted, you can turn it into a picture, such as a bar chart or pictogram, to make the results easy to see at a glance. Tidy counting now makes every chart later far easier. You will also use these counts when you start reading charts and graphs.