Statistics 1, Activity 3
Throwing a six
Students initially play a game called ‘Greedy’ in which throwing a six spells disaster and a
loss of all their accumulated points. This can be used to test the hypothesis that ‘Boys are
greedier than girls.’
The game, however, is a prelude to the main activity which involves answering the
question ‘On average, how many throws does it take to throw a six?’
In this activity students gain an understanding of ‘expectation’ as well as learning how to
calculate summary statistics when the data is given in a frequency table.
Features of this activity
 A fun game that leads into the main
activity and that will be used again in
the pathway – Probability 1
 Mathematical language developed in
context
 A practical activity that generates data
for analysis
 A brief insight into hypothesis testing
 Students will learn that even in
apparently random events, the
‘average’ number of throws is quite
predictable.
Materials and preparation
Poster: ‘Somebody once told me that boys
are greedier than girls’
Lots of dice games depend on throwing a
six.
Greedy game – instructions (greedy.docx)
‘But, on average, how many throws does it
take to throw a six?’
Introductory video (to be supplied)
Introductory PowerPoint (throw6.ppt)
‘I am not too sure, actually. What do you
think?’
Notebook file (Throwing a six) (This is a
Smartboard file.)
Page 1 of 8
Introducing the game
Somebody once told me that ‘Boys are
greedier than girls’.
If suitable, make and display a poster
similar to the one on the right.
It is meant to be provocative.
Start the lesson by saying,
‘Somebody once told me that boys are
greedier than girls…’
‘Do you agree?’
Short discussion.
‘Well, this morning we are going to find out
by playing a game called ‘Greedy’.
Now use either the Notebook file or the
Powerpoint file to explain the rules.
Hard to believe, isn’t it!
GREEDY
GREEDY?
Rules of the game:
1. Everyone stands up.
2. A normal six-sided die is rolled twice.
3. Your initial score is the sum of these
two throws.
4. You can sit down and record your score
on the score sheet.
5. Or you can remain standing and we
throw the die again.
6. If the die is a SIX, you lose all of your
score, sit down and record your score
as ZERO.
‘Sometimes you have to know when to
stop…’
7. If the die is not a SIX, you add this to
your score.
8. You can now sit down or the game
proceeds as before.
9. The aim is to score as many as
possible.
Warning
If you are too GREEDY and always choose
to remain standing, you will eventually
score ZERO.
Page 2 of 8
Collecting the data
The students play five rounds. At the end of the fifth round each student adds up the
score for the five rounds. The object of the game is to score as many as possible.
Greedy people tend to score low.
As always, it is a good idea to discuss which average is the most appropriate but the
‘choice’ of average can lead to different conclusions.
If you are using this game to compare male and female results then it is appropriate to
use a back-to-back stem and leaf plot, as shown below. Beware – this is unsorted data!
Female
Male
(1)
0
0
01720
(5)
(2)
24
1
732
(3)
(2)
82
2
743864
(6)
(4)
9082
3
5721
(4)
(6)
955001
4
(3)
746
5
602
(3)
(2)
01
6
6
(1)
(3)
474
7
0
(1)
Total
Total
(23)
Female
Male
8
(23)
Now sort the data:
(1)
0
0
00127
(5)
(2)
42
1
237
(3)
(2)
82
2
344678
(6)
(4)
9820
3
1257
(4)
(6)
955100
4
(3)
764
5
026
(3)
(2)
10
6
6
(1)
(3)
744
7
0
(1)
Total
(23)
8
(23)
Total
Page 3 of 8
Discuss any obvious differences in the data before finding any summary statistics.
In the example given, the summary statistics are:
Statistic
Female
Male
Mean
43.4
28.0
Mode
40, 45 (bimodal)
0, 24 (bimodal)
Minimum
0
0
Lower quartile
30
12
Median
41
26
Upper quartile
57
37
Maximum
77
80
Range
77
80
IQR
27
25
Low outliers
nil
nil
High outliers
nil
80
Now encourage your students to support or disagree with the suggestion that ‘Boys are
greedier than girls’.
Three important questions to discuss
‘In the last game, the key to making a high
score was anticipating when, on average,
you might get a six.’
‘Throwing a six is important in lots of board
games, so on the evidence so far, how
many throws do you think it takes to throw
a six?’
So, on average, how many throws do you
think it takes to throw a six?
Are you more likely to get your first six on
the first throw? The second throw? The
third throw? What do you think? Is this the
same question?
Record their estimates.
‘Also, do you think you are more likely to
get a six on the first throw? The second
throw? The third throw? …’
‘Is this the same question?’
Page 4 of 8
Record your students’ initial thoughts.
Now give everyone a single die (or work in
pairs) and ask them to carry out an
experiment to generate some data that will
help. Let everyone have around ten goes.
Record their results on a stem and leaf
plot, or a dot plot, or even make a large
tally chart. You will have quite a lot of data!
Summarise their results and refer to
this as the ‘wisdom of the crowd’.
Summarising the data
Now begin the sorting process by rewriting
the data in a frequency table as shown
below.
It is still difficult to draw any immediate
conclusions, so at this point it is a good
idea to draw a line graph.
The shape of this graph indicates the data
has a positive skew.
Page 5 of 8
Discuss with the group how to calculate the
mean from a frequency diagram. Make
sure they understand what to do and why!
More key measures
Page 6 of 8
Are there any outliers?
This gives your students a chance to use
the understanding of outliers introduced in
Activity 1, to decide if a student is
particularly unlucky.
In this case there seem to be several high
outliers but no low outliers. Why is that?
How does this relate to the shape of the
box plot?
Page 7 of 8
Matching histograms and boxplots
Match each histogram with its corresponding boxplot, by writing the letter of the boxplot in
the space provided.
Page 8 of 8