Go back to L3 online home page.

This is the course page for your Level 3 mathematics shape and space workshop. You can follow the links below to access the resources you need for this session.

Please have your ILP to hand as you work through these activities.

Before the session, please read HO1 Data Handling.

There are a series of links and videos below that you can refer to after the session, covering the topics you will be working on. Click the name of the topic to access the link/ video.

The Joy of Stats (BBC 4)

Toggle Content goes here

Mean, median and mode (Khan Academy)

Academy)

Real functions and graphs (Open University)

Standard deviation (Khan Academy)

Misleading statistics (TED-ed)

Scientific calculator course

Here is a link to a free course teaching you how to use a scientific calculator which will help you as you progress through the course.

### Session PowerPoint

The link to the PowerPoint is shown below:

### R1 Probability – true or false?

### R2 Sampling

Two learners are planning a survey among their fellow learners to find out what sort of things people have for breakfast and whether they eat breakfast in the canteen.

They are feeling ambitious and want to ask 100 learners.

They are discussing where they should find their sample of 100 learners. They come up with the possibilities listed on the accompanying sheets.

Discuss each method proposed, and rate it on a traffic light system, as bad, OK or good.

The ratings should be for:

- Ease of collection
- Lack of bias
- Other issues – any other negative or positive that you come up with

### R3 – An average exercise

Look at the exercise on averages below, which has been completed by another learner.

Go through it and correct all the errors made on a piece of note paper.

Write comments against each error that would help the learner who completed it to understand the mistakes they have made.

1. Find the median of the set of numbers: 2, 5, 7, 8, 9, 12

Answer: *There are 6 numbers so the median is the third which is 7*

2. Find the median of the set of numbers: 4, 7, 8, 8, 9, 12

Answer: *Median is 8.5*

3. Find the median of the set of numbers: 3, 6, 12, 15, 11, 21, 15, 16, 22

Answer: *Median is 11*

4. Find the mean of the set of numbers: 3, 11, 12

Answer: *Mean is 11*

5. Find the mean of the set of numbers: 0, 0, 0, 1, 2, 2, 3, 3, 5, 5

Answer: *Mean is 21 ÷** 7 = 3*

6. Find the mode of the set of numbers: 1, 3, 1, 3, 1, 2, 3, 4, 4, 4, 1, 2

Answer: *Mode is 4*

### R4 Statements to evaluate

Are the statements below justified by the data?

Explain why you think each either is or isn’t justified.

### R5 Variance and standard deviation

### R6 Grouped and cumulative frequency distributions

You will find 4 sets of cards (A, B, C and D) in the document below.

- Match the frequency graphs, the statements, the cumulative frequency graphs and the box plots.
- When you are sure you have a correct combination, stick them on a poster and write an explanation of how you know they match.

### R7 Grouped frequencies with unequal intervals

### R8 Grouped frequencies with unequal intervals

Match together the scattergram with Pearson’s correlation coefficients.

### R9 Probability

Watch the video below on Pascal’s Triangle:

The probability jigsaw below needs to be printed out and cut into pieces. Then, arrange the pieces into an equilateral triangle by matching the probability statements and answers on the edges of each piece.

You can see the completed triangle (answers) below.

### R10 Combined probability

**HO6 Spinners**

Now try some more activities on probability below:

### R10 Probabilities using relative frequency

**HO9 – Holiday planning**

Sally is planning a fortnight’s winter sun holiday next February, and is looking for somewhere warm and dry. She would like somewhere where the temperature is likely to be at least 20^{0}C. and where rain can be expected on no more than 3 of her 14 days away.

Use the information below to inform Sally of the likelihood of each resort meeting her requirements, and which one she might choose. Make sure you point out any limitations to your calculations.