Collect & organise data (tally & tables)
Theory
Collecting and organising data is a Year 3 statistics skill: asking a clear survey question, recording the answers with tally marks counted in groups of five, then tidying them into a frequency table. This page explains how to make and read tally marks, build a frequency table, and use it to find totals, the most and least common category, how many more, and a missing count. Curriculum: VC2M3ST01 / AC9M3ST01.
Data is the information we collect when we ask a question and record the answers, like counting votes or favourite things. A survey question should be clear and list the choices. Each choice is a category, such as apple, banana or mango. An other category lets everyone answer, even if their choice is not listed.
Tally marks are a quick way to keep count. Draw one stroke for each thing you count. Count in groups of five: four upright strokes, then a fifth stroke drawn diagonally across them to close the group. A closed group always means \(5\).
A frequency table organises the data. It has a column for the categories, a column for the tally, and a column for the frequency. The frequency is how many times each category was counted. Adding every frequency gives the total. The biggest frequency is the most common category.
Tally marks are counted in fives, and a frequency table is read by adding and subtracting.
How to collect and organise data
- Ask a clear question. Ask one question that lists the choices, such as "Which fruit do you like best: apple, banana, mango or other?"
- List the categories. Write each choice in the table, and add an "other" category so nobody is left out.
- Tally as you go. Make one stroke for each answer, closing every fifth stroke with a diagonal to form a group of five.
- Count the frequency. Count each tally by fives, add the leftover strokes, and write the number in the frequency column.
How to read a frequency table
- Find the most and least. The largest frequency is the most common category; the smallest is the least common.
- Add for totals. Add every frequency for the total. For "A or B", add just those two rows.
- Subtract to compare. For "how many more" or "how many fewer", take the smaller count from the bigger one. For "the rest", take the counts you know away from the total.
| \(\text{three closed groups}\) | \(=\) | \(5 + 5 + 5 = 15\) |
| \(\text{two leftover strokes}\) | \(=\) | \(2\) |
| \(15 + 2\) | \(=\) | \(17\) |
The tally shows \(17\) birds.
| \(16\) | \(=\) | \(5 + 5 + 5 + 1\) |
| \(\text{groups of five}\) | \(=\) | \(3\) |
| \(\text{extra strokes}\) | \(=\) | \(1\) |
Draw \(3\) closed groups of five, then \(1\) more stroke.
| \(\text{basketball}\) | \(=\) | \(5 + 5 + 2 = 12\) |
| \(6 + 10 + 12 + 3\) | \(=\) | \(31\) |
Basketball is \(12\), and \(31\) students voted altogether.
(i) Which season was the most popular, and which was the least popular?
(ii) How many more students chose summer than winter?
(iii) How many students chose autumn or winter?
| Season | Frequency |
|---|---|
| Summer | 10 |
| Autumn | 4 |
| Winter | 6 |
| Spring | 5 |
| \(\text{largest}\) | \(=\) | \(10 \to \text{summer}\) |
| \(\text{smallest}\) | \(=\) | \(4 \to \text{autumn}\) |
| \(10 - 6\) | \(=\) | \(4\) |
| \(4 + 6\) | \(=\) | \(10\) |
(i) Summer was the most popular and autumn the least popular.
(ii) \(4\) more students chose summer than winter.
(iii) \(10\) students chose autumn or winter.
| \(9 + 7 + 4\) | \(=\) | \(20\) |
| \(28 - 20\) | \(=\) | \(8\) |
Add the counts you know, then take them away from the total: \(8\) students chose other.
A: "Do you like ice blocks?"
B: "Which ice block flavour do you like best: lemon, lime, raspberry, cola or other?"
Question A only gets yes or no, so it cannot tell Tom which flavour is the favourite.
Question B is better. It asks about flavours, lists the categories, and has an other choice so every student can answer.
Common pitfalls
Frequently asked questions
What are tally marks?
Tally marks are strokes used to count things quickly. You draw one stroke for each item and count in groups of five, with the fifth stroke drawn diagonally across the first four.
How do you count tally marks?
Count the closed groups of five first, then add the leftover strokes. Three closed groups and four more strokes make \(5 + 5 + 5 + 4 = 19\).
Why is the fifth tally mark drawn across the others?
The diagonal fifth stroke closes a group of five. Grouping in fives makes a long count much faster to add up, because you can count by fives.
What is a frequency table?
A frequency table organises collected data. It has a column for the categories, a column for the tally, and a column for the frequency, which is how many times each category was counted.
How do you find the total in a frequency table?
Add up every frequency. If the counts are \(7, 5, 3\) and \(4\), the total is \(7 + 5 + 3 + 4 = 19\).
What makes a good survey question?
A good survey question is clear, asks about one thing, and lists the choices, with an other choice so everyone can answer. "What is your favourite colour: red, blue, green or other?" is a good question.
How do you find a missing count when you know the total?
Add the counts you know, then subtract that from the total. If \(30\) students were asked and the known counts add to \(24\), the missing count is \(30 - 24 = 6\).