ACARA v9 CONTENT DESCRIPTION “acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets”
Statistics does not begin with numbers; it begins with a question worth asking. What fruit do children like best? How many pets does each family have? Which day is busiest? The question decides everything that follows — what to collect, from whom, and how to record it. A clear question keeps a survey honest and focused, while a vague one gathers a muddle. This unit takes a child through the first half of every statistical investigation: deciding what to collect and writing it down in a form that can later be read and graphed.
Categorical or numerical?
Data comes in kinds. Names and groups are categorical; counts are numerical.
Is "favourite sport" categorical (a name or group) or numerical (a count)?
Two kinds of data
Before collecting, it helps to know which kind of data a question will produce. Categorical data comes as names or groups — favourite sport, eye colour, type of pet — answers you sort into categories. Discrete numerical data comes as counts — number of siblings, books read, goals scored — answers that are whole numbers. Telling the two apart matters because they are recorded and later graphed differently. The quick test is to ask whether the answer is a word that names a group or a number you reach by counting. Naming the kind of data is the quiet decision that makes the rest of the investigation tidy.
The tally counter
As each answer comes in, add a tally mark. Every fifth mark crosses the four.
Press a fruit each time someone answers. Tally marks record the count as you go.
Tally as you go
When answers arrive one at a time, a tally is the natural way to keep count without losing track. Each answer adds a single mark beside its category, and every fifth mark is drawn across the previous four to make a bundle of five. This grouping is the same bundling idea from place value, and it is what makes a long tally readable at a glance: counting bundles of five and then the leftovers is far faster than counting forty separate strokes. Recording in real time, as you observe, is a core data skill — it keeps the count accurate even when the answers come quickly.
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 marks back as numbers
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. A tally of two bundles and three singles is thirteen. 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 is what connects the messy act of collecting to the tidy number that goes into a table.
The frequency table
A frequency table turns tally marks into a tidy count for each category.
A frequency table lists each category, its tally, and the number that tally stands for. Reveal the total to check.
From tally to a tidy table
The frequency table is where collected data becomes organised: each row pairs a category with its tally and the frequency that tally stands for. It is the standard way to record data, on paper or in a spreadsheet, and its great virtue is that it can be checked — the frequencies should add up to the total number of people or things counted. A spreadsheet does the same job on a screen, with a column of categories and a column of counts, and makes totalling and later graphing effortless. The table is the bridge between gathering the data and making sense of it.
Good question, right method
Data must be gathered in a way that fits the question being asked.
How should this data be gathered? Pick the method that fits the question.
Collecting to fit the question
Different questions need different ways of collecting. Favourite fruit is gathered by asking and tallying; the number of pets by asking and writing the number; the busiest canteen day by counting customers each day; car colours by observing and tallying at the roadside. Choosing a method that fits — observing, asking, or accessing an existing data set — is part of acquiring data well. A method that does not match the question, like measuring with a ruler to find a favourite colour, gathers the wrong thing entirely. Good data collection is deliberate, not accidental.
The missing count
Every frequency table adds up to the total. Use that to find a missing count.
The frequencies must add to 10. 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. 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, answers tallied and read, and a frequency table that adds up, the data is ready for the next step — turning these counts into graphs and reading what they say, which is the next Statistics unit.
Quick self-check
1. Which of these is a categorical variable?
2. A tally shows one crossed group of five and two more marks. The count is...
3. Which is the best way to record how children travel to school?
4. "Number of goals scored" is which kind of data?
5. In a class of 10, apple has 4 and banana has 4. Cherry must be...