Plan & conduct a statistical investigation
Theory
Planning and conducting a statistical investigation is a Year 4 statistics skill built on the data cycle: pose a clear question, collect and organise the data in a frequency table, display it in a picture graph or column graph, then interpret the results. This page shows how to write a fair survey question, choose whether to survey or observe, and read what the display tells you. Curriculum: VC2M4ST03 / AC9M4ST03.
A statistical investigation is a plan for answering a question with data. You work through the same five steps each time, called the data cycle: pose, collect, organise, display and interpret.
You start by posing a question. A good survey question is clear, says who is being asked, is fair so it does not push one answer, and gives categories to choose from, like "walk, car, bus, bike or other". A leading question, such as "Isn't the bus the best way?", pushes one answer and is not fair. Next you collect the data by the best method: observe and tally real things, or ask a survey question and record each answer.
Then you organise the answers into a frequency table with categories, a tally and a count. You display the counts in a picture graph or column graph, and finally interpret the results by finding the total, the most and least common category, and how many more, and writing a conclusion.
Every statistical investigation follows the same five steps, and a few checks keep the data honest.
- Good question — clear, about one thing, says who is asked, not leading, and lists the categories with an "other" choice.
- Right method — survey people for opinions and choices; observe and tally for things you can watch, such as cars, birds or eye colours.
- Tally in fives — four upright strokes and a diagonal fifth make a group of \(5\); count the groups by fives, then add the extra strokes.
- Count everyone once — the frequencies should add up to the number of people or things in the investigation.
How to plan and conduct an investigation
- Pose the question. Write a clear, fair question that names the group and gives categories, such as "Which way do you travel to school: walk, car, bus, bike or other?"
- Collect the data. Pick the method that matches the question. Observe and tally real things, or ask each person the survey question and record the answer.
- Organise the data. Sort the answers into a frequency table with categories, a tally and a count. Check the counts add up to the total.
- Display the data. Draw a picture graph, where each picture stands for a number, or a column graph, where the height shows the count.
- Interpret the results. Read the graph to find the total, the most and least common category, and how many more one category has than another. Write a conclusion that answers the question.
A: "Isn't handball the best game?"
B: "Which game do you most like to play at recess: tag, handball, soccer, skipping or other?"
Question A is a leading question: it pushes everyone towards handball, so the answers would not be honest.
Question B is better. It names the topic, lists the categories and has an "other" choice, so every answer can be recorded.
"The best food" is too wide: it does not say who is asked or which foods to choose from.
A better question is: "Which canteen lunch do students in 4M like most: pies, sushi, wraps, pasta or other?" It says who (students in 4M), what (canteen lunch) and gives the choices.
(i) The kinds of birds that visit the school garden at lunch.
(ii) Each student's favourite season.
(i) Observe: watch the garden and tally each kind of bird you see. Birds cannot answer a survey!
(ii) Survey: a favourite is an opinion, so ask each student and tally the answers.
(i) How many ride a bike?
(ii) How many complete groups of five are in the car tally?
| \(10 + 7 + 3\) | \(=\) | \(20\text{ recorded}\) |
| \(25 - 20\) | \(=\) | \(5\) |
| \(7\) | \(=\) | \(5 + 2\) |
(i) \(5\) students ride a bike.
(ii) \(1\) complete group of five, with \(2\) strokes left over.
(i) How many more students walk than ride a bike?
(ii) For how many ways of travelling did more than \(4\) students choose it?
| \(10 - 5\) | \(=\) | \(5\) |
| \(\text{columns above 4}\) | \(\text{walk } 10,\ \text{car } 7,\ \text{bike } 5\) |
(i) \(5\) more students walk.
(ii) \(3\) ways (walk, car and bike). The bus column, at \(3\), is not more than \(4\).
| \(10 + 7 + 3 + 5\) | \(=\) | \(25\) |
| \(\text{largest}\) | \(=\) | \(10 \to \text{walk}\) |
All \(25\) students are counted. Walking is the most common way to travel, and the bus is the least common. A conclusion: "More students in 4M walk to school than travel any other way."
A: Draw a column graph and say what it shows.
B: Write the question "Which sport do you like best: netball, soccer, cricket or other?"
C: Count the tallies and write the totals in a table.
D: Ask each student and make a tally of the answers.
Follow the data cycle: pose, collect, organise, display and interpret.
| \(\text{pose}\) | \(B\) | |
| \(\text{collect}\) | \(D\) | |
| \(\text{organise}\) | \(C\) | |
| \(\text{display and interpret}\) | \(A\) |
The order is B, D, C, A.
Common pitfalls
Frequently asked questions
What is a statistical investigation?
A statistical investigation is a plan for answering a question with data. You pose a clear question, collect and organise the data, display it in a graph, then interpret what it shows.
What are the steps of the data cycle?
The data cycle has five steps: pose a question, collect the data, organise it in a frequency table, display it in a picture graph or column graph, and interpret the results.
What makes a good survey question?
A good survey question is clear, says who is asked, is fair so it does not push one answer, and gives categories that cover everyone. For example: Which way do you travel to school: walk, car, bus, bike or other?
What is a leading question?
A leading question pushes a person towards one answer, such as "Isn't the bus the best way?" It is unfair, so the data collected will not be honest. Ask a neutral question instead.
When should you observe instead of asking a survey question?
Observe when you can watch and count the thing itself, such as cars passing the gate or birds in a garden. Ask a survey question when you want people's choices or opinions.
How do you display data from a survey?
First organise the counts in a frequency table, then draw a picture graph, where each picture stands for a number, or a column graph, where the height of each column shows the count.