1. Throwing a six

2. Lots of dice games depend on throwing a six. ‘But, on average, how many throws does it take to throw a six?’ ‘I am not too sure, actually. What do you think?’ 2

3. Somebody once told me that ‘Boys are greedier than girls’ Hard to believe, isn’t it?! 3

4. ‘Sometimes you have to know when to stop…’ Greedy? 4

5. 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. 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. Greedy? Rules of the game 5

6. Recording sheet Greedy? GameScore 1 2 3 4 5 Total 6

7. Greedy? The results 012345678012345678 7

8. 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? 8

9. ‘But on average, how many throws does it take to throw a six?’ ‘I am not too sure, actually. What do you think?’ Lots of dice games depend on throwing a six. 9

10. On average, we think it takes … throws to throw a six. On average, how many throws does it take to throw a six? 01230123 Our initial thoughts 10

11. On average, it takes … throws to throw a six. On average, how many throws does it take to throw a six? 01230123 Our experimental data 11

12. How can we summarise our data when it is in this form? On average, how many throws does it take to throw a six? Summarising our experimental data 12

13. Firstly, by looking at the shape of the data: 13

14. Secondly, by looking at the key measures in the data: The total number of goes was 118 (105 + 12 + 1) (n = 118) The most common answer was 1 – so the mode is 1 The middle results are number 59 and 60 (why?) which are both 4 (how do I know?) – so the median is 4 The mean needs more work – any ideas? 14

15. Calculating the mean from a frequency table 1 + 1 + 1 + … 22 times, so 22 x 1 2 + 2 + 2 + … 15 times, so 15 x 2 Mean = 667 118 = 5.7 (to 1dp) 15

16. In a previous activity we talked about five key measures as an effective way of describing a distribution of results. We already have three of these measures: minimum 1 median 4 maximum 32 The median splits the data into two groups of 59. The middle number of the lower group (30th number) is 2 and this called the lower quartile. The middle number of the upper group (89th number) is 7 and this called the upper quartile. This enables us to add a box plot to our earlier line graph. More key measures minimum lower quartile median upper quartile maximum 124732 16

17. Firstly by looking at the shape of the data: Can you explain why the box plot looks like this and what it is telling us about the data? 17

18. Lower quartile 2 Upper quartile 7 IQR 5 1.5 x IQR 7.5 Low outliers n/a High outliers > 14.5 Can you explain why there seem to be 10 high outliers and no low outliers? How does this relate to the shape of the box plot? Are there any outliers? 18

19. Core Maths Support Programme 60 Queens Road Reading RG1 4BS E-mail cmsp@cfbt.com Call 0118 902 1243