1 of 26

Not Your Average Lesson

Bryn Jones

@brynspiration

2 of 26

Session Aims

  • Why do we use averages?
  • Mean, mode, median… which should we use?
  • How do averages link to histograms?
  • What makes a good statistical task?

Not Your Average Lesson

2

2023

Stuff you can use!

3 of 26

Averages

A fair representation/summary

  • It’s useful to summarise data with just some headline figures.

​

  • “The average score on a test was 58%” is more useful than a list of 30 scores.

An estimation of a population

  • A sample average acts as an estimate for a population’s average

​

  • “In Britain, the average woman is 162.4 cm tall, and the average man is 174.4 cm tall.” When was the list time you were measured?

Not Your Average Lesson

3

2023

 

 

4 of 26

Averages and Dot Plots

Number of dentist visits in a year

Not Your Average Lesson

4

2023

N=20

5 of 26

Task 1

Dot Plots

Not Your Average Lesson

5

2023

6 of 26

Task 1 Answers

Not Your Average Lesson

6

2023

7 of 26

Hands Up!

Do you consider yourself to be a mathematician?

Not Your Average Lesson

7

2023

Do you consider yourself to be a statistician?

8 of 26

A typical averages task

Not Your Average Lesson

8

2023

9 of 26

What makes a good averages task?

  • Set in a real-life context.
  • Gets students thinking about which average they are using, rather than merely the calculation.
  • Encourages thought about whether they are calculating an average, or estimating a population average.
  • Messy.

Not Your Average Lesson

9

2023

10 of 26

Business - Salaries

Not Your Average Lesson

10

2023

Apprentices

£19,000

£19,000

​

Core Team

£25,000

£25,000

£28,000

£32,000

£33,000

​

​

Managers

£45,000

£49,995

Owner

£198,000

Join our team! Our average salary is £47,000.

11 of 26

Task 2

Which Average?

Not Your Average Lesson

11

2023

12 of 26

More or Less

Not Your Average Lesson

12

2023

13 of 26

More or Less

Questions

  • Initially, the clip says "the mean average waiting time has always been longer than the median".

​

  • Why might that be?

​

  • Sketch a dotplot.

Not Your Average Lesson

13

2023

  • Which average is the more appropriate to quote?

14 of 26

Histograms and Stem-and-Leaf

Not Your Average Lesson

14

2023

15 of 26

Task 3

Histograms

Not Your Average Lesson

15

2023

16 of 26

Core Maths

  • Be able to select and calculate appropriate measure of central tendency (OCR Spec)
  • Interpret, analyse and compare the distributions of datasets… through appropriate measures of central tendency. (Edexcel spec)
  • Calculating/identifying mean, median… and reaching conclusions based on these measures. (AQA spec)

Not Your Average Lesson

16

2023

17 of 26

Core Maths

Not Your Average Lesson

17

2023

https://www.stem.org.uk/resources/elibrary/resource/76319/skew-histograms

18 of 26

Other Fun Tasks

  • Central Tendency by Don Steward (Students generate data- messy and gets to the question of “which average?”)

Not Your Average Lesson

18

2023

19 of 26

Other Fun Tasks

  • Interactive App

Not Your Average Lesson

19

2023

20 of 26

Other Fun Tasks

  • Dot plot generator

Not Your Average Lesson

20

2023

21 of 26

Conkers – A Statistical Prompt

Not Your Average Lesson

21

2023

22 of 26

Conkers – A Statistical Prompt

Not Your Average Lesson

22

2023

23 of 26

Conkers – A Statistical Prompt

Not Your Average Lesson

23

2023

24 of 26

Other Fun Tasks

Conkers

What questions can we ask?

What questions can we answer?

What questions can’t we answer?

Not Your Average Lesson

24

2023

25 of 26

Any Questions?

Not Your Average Lesson

25

2023

26 of 26

Thank you

Bryn Jones

​

brynrichardjones@gmail.com

​

@brynspiration

​

Not Your Average Lesson

26

2023