Guided statistical investigations
Theory
Guided statistical investigations are a Year 3 statistics skill: using data to answer a question of interest. This page shows the steps — ask a question, collect the data by survey or observation, organise it in a table, display it in a graph and answer the question — and how to write good survey choices, tell categorical data from numerical data, and ask a fair group. Curriculum: VC2M3ST03 / AC9M3ST03.
A statistical investigation uses data to answer a question of interest, such as "Which game should we buy for the sports shed?" You follow the same steps each time: ask a question, collect the data, organise it, display it and answer the question.
Data can be collected by a survey (asking people a question) or by observation (watching and keeping a tally). A good survey question is clear and lists choices that do not overlap, with an "other" choice so everyone can answer. Categorical data is answers in groups or words, like favourite colour. Numerical data is answers that are numbers, like the number of pets.
The results are only fair for the group you asked. Asking only your friends, or only one team, may give a different answer from the whole class. A conclusion answers the question using the data, and it often leads to a new question.
A statistical investigation follows the same steps every time.
- Good question — clear, about one thing, not leading, with choices that do not overlap and an "other" choice.
- Survey or observe — survey people for choices and opinions; observe and tally things you can watch.
- Categorical or numerical — categorical data is groups (colours, sports); numerical data is numbers (pets, siblings).
- Fair group — ask everyone, or a mix, so the results are like the whole group you want to know about.
How to carry out a guided investigation
- Ask a question of interest. Choose something you want to find out, and write a clear survey question with choices that do not overlap.
- Collect the data. Ask everyone in the group (survey) or watch and tally (observation).
- Organise the data. Put the tallies and counts in a frequency table and check the total.
- Display the data. Draw a picture graph or a column graph with a title, labels and a scale that starts at \(0\). When the counts are big (in the hundreds), choose a column graph: one picture or one tally mark for every single thing would take far too long to draw and read.
- Answer the question. Say what the data shows, and think of a new question to ask next.
An investigation starts with a question of interest that data can answer.
First, ask a clear question, such as: "Which new game would you most like for the sports shed: hoops, frisbee, skipping ropes or other?" Then they can collect everyone's answers.
A student who read \(2\) books could tick two boxes, and so could a student who read \(4\). A student who read \(8\) books has no box at all.
The choices overlap and do not cover everyone. Better choices: \(0\) to \(2\), \(3\) to \(5\), \(6\) or more.
(i) How many people are in each car at morning drop-off.
(ii) Each student's favourite fruit.
(i) Observe: watch the cars and tally how many people are in each one.
(ii) Survey: ask each student, because a favourite is a choice only they can tell you.
| Categorical (groups) | Numerical (numbers) |
|---|---|
| favourite sport | number of teeth lost |
| hair colour | number of letters in your name |
Answers that are names of groups are categorical. Answers that are counts are numerical.
| \(9 + 6 + 4 + 2\) | \(=\) | \(21\) |
| \(\text{largest}\) | \(=\) | \(9 \to \text{hoops}\) |
\(21\) students answered. Hoops had the most votes, so the answer to the question is: buy hoops.
A title that says what it shows, a label on each axis, a scale that starts at \(0\) and goes up in equal steps, and columns of the same width with gaps between them, because each game is a separate category. A graph shows the biggest group faster than a table; a table shows the exact numbers.
Ben's soccer friends are likely to choose soccer, so his group is not like the whole class.
No. To answer for the class, Ben should ask everyone in the class, or at least a mix of students who are not all in one group.
(i) Can 3J's results tell you what the whole school wants?
(ii) Write a new question to investigate next.
(i) No. One class may not be like the whole school, and 3K gave a different answer. To answer for the school, collect data from every class.
(ii) For example: "Which colour hoops would you like: red, blue, green or other?" A new question starts the investigation again.
Common pitfalls
Frequently asked questions
What is a statistical investigation?
It is a way of answering a question of interest with data. You ask a question, collect the data, organise it in a table, display it in a graph and use it to answer the question.
What is the first step of an investigation?
The first step is to decide on the question you want to answer and write a clear survey question with choices for people to pick from.
What is the difference between a survey and an observation?
In a survey you ask people a question and record their answers. In an observation you watch and record what happens, such as tallying the colours of cars that drive past.
What is the difference between categorical and numerical data?
Categorical data is in groups or words, such as favourite sport or hair colour. Numerical data is numbers you count, such as the number of teeth lost.
Why should a survey have an other choice?
An other choice lets everyone answer, even if their choice is not in the list, so nobody is left out of the results.
Why is asking only your friends not fair?
Your friends may like the same things as you, so their answers might not match the whole class. Ask everyone, or a mix of students, to get a fair result.