ACARA v9 CONTENT DESCRIPTION “acquire data for categorical and discrete numerical variables to address a question of interest by surveying, observing and experimenting; record the data using appropriate methods including frequency tables and spreadsheets”
A statistical investigation starts with a question worth answering by collecting data, and Year 4 makes the planning deliberate. Which season do children like best? How many siblings does each child have? Which book genre is borrowed most? Each question decides what to collect, from whom, and how to record it. The first job is still to recognise the kind of data the question will produce, because categorical and numerical answers are gathered and organised differently. A clear question and the right kind of data keep an investigation focused from the very start.
What kind of data?
Every question produces a kind of data: a name (categorical) or a count (numerical).
Is "favourite school subject" categorical (a name or group) or numerical (a count)?
Naming the kind of data
Before any survey runs, it helps to know what kind of answer it will produce. Categorical data comes as names or groups, like favourite subject, type of shoe or eye colour, answers you sort into categories. Discrete numerical data comes as counts, like goals scored or books read, answers that are whole numbers. The quick test is whether the answer is a word naming a group or a number reached by counting. This matters because the kind of data decides how it is recorded and, later, which graph fits. Naming the kind of data is the quiet decision that keeps the rest of the investigation tidy.
Run the survey
Collecting means recording each answer into its category as it arrives.
Ask each person their favourite season and add a tally. Data is collected one answer at a time.
Running a survey by tally
A survey collects answers from many people, and the tally is the natural tool for keeping count without losing track. Each answer adds one mark to its category, and every fifth mark crosses the previous four to make a bundle of five. This bundling, the same idea as place value, keeps a long survey readable at a glance. Tallying as the answers arrive, in real time, is what keeps the count accurate even when responses come quickly. A survey is just an organised way of asking the same question of everyone and recording each answer carefully.
Read the tally
Reading a tally is counting in fives, then adding the leftover marks.
Count the tally: each crossed group is five, then add the leftover marks.
Reading the marks as frequencies
A tally is only useful if it can be read back, and reading it is counting in fives. Each crossed bundle is five; the loose marks after the last bundle are added on. Two bundles and one mark make eleven. This skip-counting of fives, with the remainder added, turns the marks into a frequency — the number of times that answer occurred. Moving fluently between the marks and the number connects the act of collecting to the tidy count that goes into a table, and it is the skill every survey depends on at the end.
A two-way table
Data can be split by two categories at once, with totals down and across.
A two-way table splits data by two categories at once — here year level and how they travel. Reveal the totals.
Splitting data two ways
Year 4 adds a powerful new way to organise data: the two-way table, which sorts answers by two categories at once. A table of how children travel to school, split by year level and by walking or riding, shows both at a glance, with totals running down each column and across each row. The great check is that the totals must agree: the row totals and the column totals both add to the same grand total, because every person is counted exactly once. Two-way tables are how real data, which often has more than one feature, is organised so that patterns between the two categories can be seen.
Plan the survey
A good investigation plans how to collect the data before starting.
How should this survey be run? Choose the method that fits the question.
Planning how to collect
A good investigation plans the method before collecting anything. Favourite sport is found by asking every child and tallying; the number of siblings by asking and writing the number; the most borrowed genre by counting borrows over a week. Choosing a method that fits — surveying, observing, or experimenting — is part of acquiring data well. A method that does not match, like weighing children to find a favourite sport, gathers the wrong thing entirely. Planning deliberately, rather than collecting at random, is what separates a real investigation from a guess.
Complete the table
Every frequency table adds up to the total. Use that to find a missing count.
The frequencies must add to 18. What number fills the gap?
A table that adds up
Because every person or thing is counted exactly once, the frequencies in a table always sum to the total. That fact is a built-in check: if one count is missing, the total finds it, and if the parts do not add to the total, something was miscounted. A table of eighteen children showing summer six, autumn four and spring five must have winter three, because the four counts make eighteen. This is the same part-part-whole reasoning from Number, now guarding the accuracy of real data. With a clear question, the kind of data named, a survey tallied and read, and tables that add up, the data is ready to be graphed and interpreted, which the next Statistics unit takes on.
Quick self-check
1. Which of these is a categorical variable?
2. A tally shows two crossed groups of five and one more mark. The count is...
3. "Number of goals scored in a match" is which kind of data?
4. A frequency table of 18 people shows summer 6, autumn 4, spring 5. Winter must be...
5. Which is a good way to find the favourite sport of every child in a class?