Statistics Taster Session

Welcome to the A Level Statistics Taster Session!

We're really hoping to meet some of you in person next year! However, at this point of the year we would normally invite you to visit our department for Taster Day so that you could get to know some of us and learn about the courses we have on offer. In place of this, we've put together a lesson below which we'd like you to work your way through. We hope you enjoy!

Please follow the instructions and videos below:

Introduction

Can you think of some reasons why businesses overbook? Jot them down now and then click the video below to see if we have similar answers!

Did you know?

That's a lot of angry customers!

So why do companies overbook?

Check out this video to see what we had to say about it!

Main Activity

Case Study NYC to LHR

After years of data collection, a certain airline knows that the probability someone turns up on time for their flight from New York City to London Heathrow is 90%.

If the plane has 180 seats and sells 180 tickets, how many people are likely to board?

See if you can work out the answer and then click to watch the video for the solutions and a brief discussion!

So how do we work out the probability of each scenario described in the video above?

Watch the video to see an example and then try to work out some probabilities for yourself! You'll need the worksheet which you can access here.

Worksheet

Improving our Model

This calculating from tree diagrams is tedious though isn't it? Can you imagine trying to work out the probabilities for all 180 passengers?

Surely there's a faster method?

There is! Check out the video here and try the tasks to see if you can work out how this faster method works!

Revenue

Let's assume a ticket costs £250.

How much revenue will the airline make if they sell every ticket and don't overbook? 

Let's assume is costs them £800 for every passenger they have to bump off a flight due to overbooking.

If the airline sells 15 extra tickets (so 195 total), then what is the best and worst case scenario for their revenue?

Watch the video to see if you've got the right answers!

So how do airlines decide?

It comes down to what is the most and least likely outcomes!

Watch this short video for a discussion about the likelihood of each outcome.

Then, try adjusting how many seats the airline sells here.

Can you work out which number of seats to sell is best?

Geogeba Graph 1

See how close you were to the right answer by watching our video discussion of the solutions.

You might also find this graph helpful!

Geogebra Graph 2

Summary

Watch this video for a short 5 minute summary of what we have covered today!

What else have we learned about today?

Mathematical modelling – simplifying real world problems so we can solve them with statistics
The Binomial Distribution
Expectation and Expected Revenue

How does Statistics link to College and beyond?

A-Level Statistics covers a lot of the statistics that you'll use in other A Level courses like Biology, Psychology, Geography, Sociology. It's also useful for many University courses and for future employment. Scroll down to see more!