This document provides demonstrations of calculating the mean, median, mode, and range for various data sets. It explains how to find each average value and compares the strengths and weaknesses of each. The mean averages all values, the median ignores outliers, and the mode represents non-numerical or categorical data. Examples are worked through step-by-step and the key is to order the data before analyzing it using these different averaging methods.

1. Mean, Median, Mode & Range – Demonstration
This resource provides animated demonstrations of the mathematical method.
Check animations and delete slides not needed for your class.

2. Andy is growing flowers.
After 1 week he measures the height of the flowers.
Which group of flowers grew better?

3. To compare sets of data we use averages:
a number that is used to represent the whole group.
We could use the middle value of the group.
Middle Value
Middle Value
Using the median average the
red flowers grew better.

4. We can represent data (like flower height) using bars instead.
Using the median, which group of flowers grew better?
To help we place the data in size order.
2
3
The pink flowers grew better – they have a better median average.
Is this fair?

5. Place data in size order &
select the middle value.
Median
 Does not include every piece of data
 Ignores outliers
What can we do if there are 2 middle values?
The median is between the two middle values.

6. Two teams played darts.
Using the mean average the
adults won.
Adults: 32 points Kids: 35 points
Which team won?
To be fair, we want to calculate points scored per player, the mean average.
Total Points ÷ Number of Players
8 points per player 7 points per player

7. We can represent scores from a different dart game using bars.
Using the mean, which team won?
Total the data and divide it by the quantity.
2
The green team won – they have a better mean average.
Is this fair?
2 2 1
3 3
1
5
3

8. Place data in size order &
select the middle value.
Median
 Does not include every piece of data
 Ignores outliers
Sum data & divide by
the number of values.
Mean
 Can be distorted by outliers
 Includes all data

9. Ash was practicing darts.
She scored:
1, 5, 20, 1, 1, 1, 5, 1, 1
Is the mean a good representation of this data?
Mean = 36 ÷ 9 = 4
The mean is larger than most of the scores. This is because of the outlier 20.
Instead we can use the mode average: the most common piece of data.
Mode = 1

10. A shop recorded the flowers it sold.
pink, red, red, red, blue, pink, blue, red
Can we calculate a mean or median?
For non-numerical data,
we can calculate the mode: the most common piece of data.
Mode = Red

11. Averages: One value to represent the group.
Mean
Sum of values divided by quantity
7, 1, 4, 1, 2
Median
The middle value.
2 middle values = take the mean of those.
Mode
The most common value.
7, 1, 4, 1, 2
7+1+4+1+2
5
= 3
1, 1, 2, 4, 7
7, 1, 4, 1, 2
1, 1, 2, 4, 7
= 2
= 1
4, 5, 0, 2, 9, 1
4, 5, 0, 2, 9, 1
4+5+0+2+9+1
6
= 3.5
0, 1, 2, 4, 5, 9
4, 5, 0, 3, 9, 1
0, 1, 2, 4, 5, 9
= 3
= No Mode

14. Mr Smith gave two classes the same science test.
Which class do you think he is more proud of?
Class A
Mean = 34 marks
Median = 32 marks
Highest score = 29 marks
Lowest score = 38 marks
Class B
Mean = 33 marks
Median = 34 marks
Highest score = 71 marks
Lowest score = 15 marks
The mean & median are very similar.
However Class B has a wide range of results.
Class A were more consistent.
Range = 7 marks Range = 56 marks

15. We can represent test results using bars.
Which class was more consistent?
Class X has a bigger range:
the difference between the highest result & the lowest result.
Class X Class Y
A range represents the spread of the data, it is not an average.

16. A range only considers the highest & lowest values.
The range for Class A is greater, but the class was actually more consistent.
Class A Class B
What may be the problem using range?

17. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO
1, 0, 6, 2, 1
Mean =
= 10 ÷ 5
0, 1, 1, 2, 6
Median =
(0+1+1+2+6) ÷ 5
1
Mode = 1
Range = 6 – 0
= 6
place in
order
= 2

18. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO
7, 2, 4, 3, 9
Mean =
= 25 ÷ 5
2, 3, 4, 7, 9
Median =
(2+3+4+7+9) ÷ 5
4
Mode = No Mode
Range = 9 – 2
= 7
place in
order
= 5

19. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO
8, 3, 10, 4, 2, 6, 2
Mean =
= 35 ÷ 7
2, 2, 3, 4, 6, 8, 10
Median =
(2+2+3+4+6+8+10) ÷ 7
4
Mode = 2
Range = 10 – 2
= 8
place in
order
= 5

20. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO
6, 3, 1, 4, 7, 0, 3, 8
Mean =
= 32 ÷ 8
0, 1, 3, 3, 4, 6, 7, 8
Median =
(0+1+3+3+4+6+7+8) ÷ 8
(3+4) ÷ 2
Mode = 3
Range = 8 – 0
= 8
place in
order
= 4
= 3.5

21. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO YOUR TURN
6, 3, 1, 4, 7, 0, 3, 8
Mean =
= 32 ÷ 8
0, 1, 3, 3, 4, 6, 7, 8
Median =
(0+1+3+3+4+6+7+8) ÷ 8
(3+4) ÷ 2
Mode = 3
Range = 8 – 0
= 8
place in
order
= 4
= 3.5
Find the Mean, Median, Mode & Range for
this set of data.
3, 1, 5, 1, 1, 3, 7
Mean =
= 21 ÷ 7
1, 1, 1, 3, 3, 5, 7
Median =
(1+1+1+3+3+5+7) ÷ 7
3
Mode = 1
Range = 7 – 1
= 6
place in
order
= 3

22. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO YOUR TURN
6, 3, 1, 4, 7, 0, 3, 8
Mean =
= 32 ÷ 8
0, 1, 3, 3, 4, 6, 7, 8
Median =
(0+1+3+3+4+6+7+8) ÷ 8
(3+4) ÷ 2
Mode = 3
Range = 8 – 0
= 8
place in
order
= 4
= 3.5
Find the Mean, Median, Mode & Range for
this set of data.
5, 9, 0, 2, 11, 4, 1, 8
Mean =
= 40 ÷ 8
0, 1, 2, 4, 5, 8, 9, 11
Median =
(0+1+2+4+5+8+9+11) ÷ 8
(4+5) ÷ 2
Mode = No Mode
Range = 11 – 0
= 11
place in
order
= 5
= 4.5

23. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO YOUR TURN
6, 3, 1, 4, 7, 0, 3, 8
Mean =
= 32 ÷ 8
0, 1, 3, 3, 4, 6, 7, 8
Median =
(0+1+3+3+4+6+7+8) ÷ 8
(3+4) ÷ 2
Mode = 3
Range = 8 – 0
= 8
place in
order
= 4
= 3.5
Find the Mean, Median, Mode & Range for
this set of data.
6, 5, 1, 5, 7, 1, 3, 8
Mean =
= 36 ÷ 8
1, 1, 3, 5, 5, 6, 7, 8
Median =
(1+1+3+5+5+6+7+8) ÷ 8
(5+5) ÷ 2
Mode = No Mode
Range = 8 – 1
= 7
place in
order
= 4.5
= 5

24. Calculating MMMR
Find the Mean, Median, Mode & Range for
this set of data.
DEMO YOUR TURN
6, 3, 1, 4, 7, 0, 3, 8
Mean =
= 32 ÷ 8
0, 1, 3, 3, 4, 6, 7, 8
Median =
(0+1+3+3+4+6+7+8) ÷ 8
(3+4) ÷ 2
Mode = 3
Range = 8 – 0
= 8
place in
order
= 4
= 3.5
Find the Mean, Median, Mode & Range for
this set of data.
10, 4, 5, 7, 4, 8, 16, 4, 5
Mean =
= 63 ÷ 9
4, 4, 4, 5, 5, 7, 8, 10, 16
Median =
(4+4+4+5+5+7+8+10+16) ÷ 9
5
Mode = 4
Range = 16 – 4
= 12
place in
order
= 7

25. A 1 2 2 3 7 B 1 4 6 8 5 2 2
Calculate the Mean, Median, Mode & Range for each set of data.
Mean = 3 Median = 2
Mode = 2 Range = 6
Mean = 4 Median = 4
Mode = 2 Range = 7
C
8 10 9 7
3 0 5 6
D
8 4 3 5 2
3 6 1 0 3
Mean = 6 Median = 6.5
Mode = No Mode Range = 10
Mean = 3.5 Median = 3
Mode = 3 Range = 8
E
−5 7 8 13 5
0 6 −10 3
F
23 21 24 20 22 20
20 23 22 24 21 24
Mean = 3 Median = 5
Mode = No Mode Range = 23
Mean = 22 Median = 22
Mode = No Mode Range = 4

27. A 5 5 6 8 9 B 15 6 4 8 12 6 10
Calculate the Mean, Median, Mode & Range for each set of data.
Mean = 6.6 Median = 6
Mode = 5 Range = 4
Mean = 8.7 Median = 8
Mode = 6 Range = 11
C
9.5 8 1.5 7
4 16 2 11
D
9 11 5.5 7.2 24.8
7.2 16 8.4 13.5 10.4
Mean = 7.4 Median = 7.5
Mode = No Mode Range = 14.5
Mean = 11.3 Median = 9.7
Mode = 7.2 Range = 19.3
E
−6.6 0.7 8.2 9.9 4.7
4.2 6 −7.8 −13.4
F
58 50 60 52 57
52 57 56 58 50
Mean = 0.7 Median = 4.2
Mode = No Mode Range = 23.3
Mean = 55 Median = 56.5
Mode = No Mode Range = 10
(1dp)

29. Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk