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# Statistics - Maths of Real Life

### Introduction

In the 21st century, more data is collected about us than ever before, and as computers become more powerful, we can process, interpret and analyse large data sets to look for patterns, make predictions, and discover new ideas. Whether you study mathematics, science, social sciences or humanities, it is becoming increasingly important to have a good grasp of statistical ideas and an understanding of the maths underlying statistical methods.

These resources are designed to introduce key statistical ideas needed for advanced study. They also give opportunities to consolidate your understanding by applying it to new and engaging contexts. Try the activities to delve into the concepts of hypothesis testing, sampling, and distributions, and explore some of the fascinating and complex issues surrounding the interpretation and representation of data. Scroll down to find articles which explain key ideas and go more deeply into the concepts.

To complement each resource, there are Teachers' Resources with suggestions for how the tasks can be used in the classroom.

### Try

These resources investigate statistics concepts usually met by students aged 14-16

### Statistical Shorts

### A Population Survey

### Which Spinners?

### Counting Fish

### Data Matching

### Where Are You Flying?

### One Variable, Two Variable, Three Variable, More

### Sleep: the Silent Killer

### Do You Brush Your Teeth Every Day?

### Try more

These resources explore statistics concepts usually met by students aged 16-18

### Stats Statements

### Hypothetical Shorts

### Robin's Hypothesis Testing

### Powerful Hypothesis Testing

### Can You Find ... Random Variable Edition

### Binomial or Not?

### Binomial Conditions

### A Well-stirred Sample

### Read

These articles provide some background on key ideas in statistics and probability.

### Understanding Hypotheses

### A Probability Conundrum

### The Surveyor Who Came to Tea

### Read more

These articles invite you to explore statistical ideas in more depth.

### What Is a Random Variable, Really?

### What Is a Hypothesis Test?

### Challenging Data Tasks: The Making of "Where Are You Flying?"

*The development of these resources was made possible by donations co-ordinated by PSI from Amgen, AstraZeneca, GSK, PHASTAR and Roche. We would like to thank all contributors for their generous support.*

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### Over-booking

### Binomial Conditions

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*This pilot collection of resources is designed to introduce key statistical ideas and help students to deepen their understanding.*

In the 21st century, more data is collected about us than ever before, and as computers become more powerful, we can process, interpret and analyse large data sets to look for patterns, make predictions, and discover new ideas. Whether you study mathematics, science, social sciences or humanities, it is becoming increasingly important to have a good grasp of statistical ideas and an understanding of the maths underlying statistical methods.

These resources are designed to introduce key statistical ideas needed for advanced study. They also give opportunities to consolidate your understanding by applying it to new and engaging contexts. Try the activities to delve into the concepts of hypothesis testing, sampling, and distributions, and explore some of the fascinating and complex issues surrounding the interpretation and representation of data. Scroll down to find articles which explain key ideas and go more deeply into the concepts.

To complement each resource, there are Teachers' Resources with suggestions for how the tasks can be used in the classroom.

These resources investigate statistics concepts usually met by students aged 14-16

Age 11 to 16

Challenge Level

Can you decide whether these short statistical statements are always, sometimes or never true?

Age 14 to 18

Challenge Level

A geographical survey: answer the tiny questionnaire and then analyse all the collected responses...

Age 14 to 18

Challenge Level

Can you work out which spinners were used to generate the frequency charts?

Age 14 to 16

Challenge Level

I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

Age 14 to 18

Challenge Level

Use your skill and judgement to match the sets of random data.

Age 14 to 18

Challenge Level

Where do people fly to from London? What is good and bad about these representations?

Age 14 to 18

Challenge Level

Displaying one-variable and two-variable data can be straightforward; what about three or more?

Age 16 to 18

Challenge Level

"Too much sleep is deadly" proclaimed the newspaper headline. Is this true?

Age 14 to 18

Challenge Level

How can we find out answers to questions like this if people often lie?

These resources explore statistics concepts usually met by students aged 16-18

Age 16 to 18

Challenge Level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Age 16 to 18

Challenge Level

Some short statements about hypothesis testing: are they true, false, or somewhere in between?

Age 16 to 18

Challenge Level

How many trials should we do in order to accept or reject our null hypothesis?

Age 16 to 18

Challenge Level

How effective are hypothesis tests at showing that our null hypothesis is wrong?

Age 16 to 18

Challenge Level

Can you create random variables satisfying certain conditions?

Age 16 to 18

Challenge Level

Are these scenarios described by the binomial distribution?

Age 16 to 18

Challenge Level

When is an experiment described by the binomial distribution? Why do we need both the condition about independence and the one about constant probability?

Age 16 to 18

Challenge Level

Typical survey sample sizes are about 1000 people. Why is this?

These articles provide some background on key ideas in statistics and probability.

Age 14 to 18

This article explores the process of making and testing hypotheses.

Age 14 to 18

What do we mean by probability? This simple problem may challenge your ideas...

Age 14 to 18

This article discusses how a survey company carries out its surveys and some of the issues involved.

These articles invite you to explore statistical ideas in more depth.

Age 16 to 18

This article offers an advanced perspective on random variables for the interested reader.

Age 16 to 18

This article explores the meaning of hypothesis tests, and also some of the major difficulties in interpreting them

Age 16 to 18

How was the data for this problem compiled? A guided tour through the process.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

When is an experiment described by the binomial distribution? Why do we need both the condition about independence and the one about constant probability?