---
marp: true
theme: default
html: true
---

# Statistical investigations

Data and chance · Data

<!-- Speaker note: Students plan an investigation (question, variable, sample, bias), then summarise and report one in terms of shape, centre and spread (AC9M7ST03, nodes 1 and 2). About 40 minutes (Predict and Run 8 min · Investigate 10 min · Modify 10 min · Practise and Make 12 min). -->

---

## Today

**We are learning to** an investigation asks a question that data can answer, plans who to measure and how, collects and displays the data, describes its shape, centre and spread, and reports an answer with its limits.

- I can write a question that data can answer.
- I can plan a fair sample and name a possible bias.
- I can report what data show using shape, centre and spread, and say the limits.

<!-- Speaker note: Before class: Do the Run board yourself first. Students need the data lessons before this one (kinds of data, centre, stem-and-leaf plots, comparing data). The one idea: the answer is only as good as the question and the sample. A small, friendly sample describes that group and not the whole year (Kai's mistake). This lesson gives the shape of a whole investigation with sleep as the example. The real investigation is a class task: students choose their own question (sleep, screen time, reaction time, jumping), collect data in class, display it on the data board or a spreadsheet and write the report in the four parts of the Make task. Do at least two investigations in different contexts, so the skill transfers. A public source (the Australian Bureau of Statistics, for example) can give a second set for a social question; use it as an extension. -->

---

## Why it matters

> Do students your age sleep less on school nights? You could argue about it, or you could measure it. What would you need to decide first?

<!-- Speaker note: A **statistical investigation** goes through these stages: 1. **Ask** a statistical question: one that data can answer, with a variable you can measure ("How many hours do Year 7 students sleep on school nights?"). 2. **Plan**: decide the variable (**discrete** if counted, **continuous** if measured), the **sample** (who, and how many) and how to measure it. Look out for **bias**, where the sample or the measuring favours one answer. 3. **Collect** the data, **display** it (dot plot, stem-and-leaf plot), and **summarise** it: shape, centre and spread. 4. **Report** an answer to the question, with its limits (who was measured, how many, how). -->

---

<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**Which of these can be answered by measuring a number for each student?**

- Is sleep important?
- How many hours do Year 7 students sleep on school nights?
- Should school start later?
- Is sleep boring?

<!-- Speaker note: What happens: The first. It names a variable you can measure (hours) and a group (Year 7). The others are opinions or decisions; data can inform them but cannot answer them. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask what number you would write down for each question. -->

---

<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fdata%2Finvestigations%2Fstep-2&code=widget%3A+data%0Avalues%3A+6.5%2C+7%2C+7.5%2C+8%2C+8%2C+8%2C+8.5%2C+8.5%2C+8.5%2C+9%2C+9%2C+9%2C+9.5%2C+10%2C+10%0Arange%3A+5%2C+12%0Astep%3A+0.5%0Aedit%3A+on%0Ashow%3A+mean%2C+median%2C+range%0Alabel%3A+Hours+of+sleep+on+a+school+night%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/data/investigations/?full=step-2#step-2)

<!-- Speaker note: Click on the line to add a value. -->

<!-- Speaker note: Teacher: ask what the new value does to the median and to the range. -->

<style scoped>pre, marp-pre { font-size: 0.5em; line-height: 1.25; } section { font-size: 25px; }</style>

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* The first. It names a variable you can measure (hours) and a group (Year 7). The others are opinions or decisions; data can inform them but cannot answer them.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Variable type

**Hours of sleep is measured on a clock. Is it discrete or continuous?**

- Discrete: it is counted
- Continuous: any value in a range can occur
- Neither

* Answer: Continuous: any value in a range can occur

<!-- Speaker note: Measured quantities such as time are continuous. Counted ones, such as the number of pets, are discrete. -->

<!-- Speaker note: Teacher: ask students to name a second source of bias. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**Kai wants to know how long Year 7 students sleep. Click the line where he draws a conclusion he cannot support.**

```
 1  Kai's question: how many hours do Year 7 students sleep on school nights?
 2  He asks the 8 students in his swimming squad.
 3  Their median is 8 hours, so Year 7 students sleep 8 hours.
```

* Answer: line 3

<!-- Speaker note: Line 3: eight students from one squad are a small group and not a fair sample of Year 7. Swimmers may sleep more or less than others. The result describes his squad. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A fair sample

**Which is the fairest way to choose 20 students from Year 7?**

- Ask those who put up their hands
- Ask your friends
- Pick 20 names at random from the class lists
- Ask the first 20 students at the canteen

* Answer: Pick 20 names at random from the class lists

<!-- Speaker note: Random selection gives every student the same chance and avoids bias. -->

---

<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Compare and report



- **The best report:** Name both the centre and the spread.
- **Equal samples:** 
- **Shape:** 
- **An outlier:** 
- **Support or refute:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/data/investigations/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Comparing school nights with weekends uses centre and spread together, needs sets of the same size to be fair, and handles an outlier by checking it first. Hints, in order: School nights has 7 values; the weekend has 10. / Add three values to the school nights. For students who need more support: Give students the report in four sentence starters: My question was…, I measured…, The data show…, This is limited because… For early finishers: Repeat the investigation with a sample twice the size. How much do the median and range change? Compare it with a published data set. The hard part, on purpose: Planning before collecting. Ask students to say who they would measure and how, before looking at any numbers. When students get stuck: A student asks an opinion question. Ask: What would you write down for each person? Fix: Turn it into a variable you can measure. / A student generalises from a few friends. Ask: Would your friends be like the rest of Year 7? Fix: Say who was measured, and how they were chosen. / A student reports only the mean. Ask: How spread out are the values? Fix: Report shape, centre and spread. -->

<!-- Speaker note: Teacher: ask what the report would say with different samples. -->

---

<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Investigations

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fdata%2Finvestigations%2Fstep-5&code=widget%3A+data%0Avalues%3A+6.5%2C+7%2C+7.5%2C+8%2C+8%2C+8%2C+8.5%2C+8.5%2C+8.5%2C+9%2C+9%2C+9%2C+9.5%2C+10%2C+10%0Arange%3A+5%2C+12%0Astep%3A+0.5%0Aedit%3A+on%0Ashow%3A+mean%2C+median%2C+range%0Alabel%3A+Hours+of+sleep+on+a+school+night%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/data/investigations/?full=step-5#step-5)

<!-- Speaker note: What this step is for: Summaries, variable types and a median review, mixed; calling a small friendly sample the whole group is the planted slip; the median review keeps the centre fresh. -->

<style scoped>pre, marp-pre { font-size: 0.5em; line-height: 1.25; } section { font-size: 25px; }</style>

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## The mean

**Hours of sleep: 7, 8, 9. What is the mean?**

* Answer: 8

<!-- Speaker note: (7 + 8 + 9) ÷ 3 = 8 hours. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Discrete

**Which variable is discrete?**

- A student's height
- The time to run 100 m
- The mass of a school bag
- The number of siblings a student has

* Answer: The number of siblings a student has

<!-- Speaker note: Counted quantities are discrete. The others are measured. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A biased survey

**A survey asks only students who walk to school about how long they sleep. What is the problem?**

- The sample is too big
- Nothing
- Sleep cannot be measured
- The sample is biased: walkers may not be like everyone else

* Answer: The sample is biased: walkers may not be like everyone else

<!-- Speaker note: A sample must represent the group the question is about. -->

<style scoped>pre, marp-pre { font-size: 0.5em; line-height: 1.25; } section { font-size: 27px; }</style>

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Review: median

**Review: what is the median of 4, 7, 9, 12, 13?**

* Answer: 9

<!-- Speaker note: The middle value of the five is 9. -->

---

<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: your investigation

Now write a report of four short parts: the question, the plan (variable, sample and how you would choose it), what the data show (shape, centre, spread), and the limits of your answer.

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/data/investigations/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Building a data set to a target and writing the report in the four stages puts the whole cycle together. Hints, in order: Click the line to add values, or type them in the box. / A median of 8.5 needs values on both sides of it. -->

<!-- Speaker note: Teacher: ask students to swap reports and find the limits the author left out. -->

---

<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**A survey asks only the first 10 students into school how they travel. Give one reason it may not represent the school.**

* Students who arrive early may travel differently (for example, by bus or parent drop-off), so the sample is biased.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: This completes AC9M7ST03, with a class investigation. Where it leads: comparing larger data sets, histograms and scatter plots (Year 8). -->