1. Statistics 2

2. Variables Discrete Continuous Quantitative (Numerical) (measurements and counts) Qualitative (categorical) (define groups) Ordinal (fall in natural order) Categorical (no idea of order) We are only going to consider quantitative variables in this AS

3. Quantitative Discrete Many repeated values Age groups Marks Continuous Few repeated values Height Length Weight

4. Qualitative Categorical Gender Religious denomination Blood types Sport’s numbers (e.g. He wears the number ‘8’ jersey) Ordinal Grades Places in a race (e.g. 1st, 2nd, 3rd)

5. Collecting data Tally chartsStem and leaf plots How we collect the data usually depends on what question we wish to answer.

6. Tally chart If we were asking people what they had for breakfast we might set up a table like this…

7. Tally chart BreakfastTallyFrequency Toast Cereal Eggs Porridge Rice No breakfast

8. Tally Chart We use a tally chart when data fits easily into categories.

9. Stem and leaf plot A stem and leaf plot sorts data that has few values the same.

10. Example The number of punnets of strawberries picked by Carol over a 17-day period. (This example is in your text book) 65 73 86 90 99 106 45 92 94 102 107 107 99 83 101 91

11. Example Set up a ‘stem’ based on the fact that the numbers picked are between 40 and 110

12. Example Stem 4 5 6 … 10

13. Example The first number is 65 and the next is 73. They are recorded like this

14. Example StemLeaf 4 5 65 73 …

15. Example StemLeaf 45 5 65 73 86 3 90 9 2 4 7 9 1 106 2 7 7 1

16. Sort the data in order StemLeaf 45 5 65 73 83 6 90 1 2 4 7 9 9 101 2 6 7 7

17. Lowest and highest values StemLeaf 45 = 45 5 65 73 83 6 90 1 2 4 7 9 9 101 2 6 7 7 = 107

18. Median and quartiles StemLeaf 45 = 45 5 65 73 83 6 = 84.5 90 1 2 4 7 9 9 101 2 6 7 7 = 107

19. Median and quartiles StemLeaf 45 5 65 73 83 6 90 1 2 4 7 9 9 101 2 6 7 7

20. 5- number summary Lowest = 45 LQ = 84.5 Median = 94 UQ = 101.5 Highest = 107 StemLeaf 45 5 65 73 83 6 90 1 2 4 7 9 9 101 2 6 7 7 Median and quartiles

21. Pictures that tell a story Drawing a picture of our data. Our data is discrete and hence a bar graph is an appropriate way of showing our ‘picture’.

22. A bar graph

23. We use a bar graph (spaces between bars) because we are dealing with discrete data (counted data, many repeated values)

24. Bar graph A bar graph gives us a picture of the data and we can easily see many features of our data.

25. Bar graph Lowest = 3 letters Highest = 8 letters Mode = 5 letters The graph is approximately symmetrical and uni-modal (has only one mode)

26. Bar graph To find out how many were surveyed, you add the frequencies together.

27. Pie graph Each category makes up a certain percentage of the ‘pie’. A pie graph does not tell us how many were in the data set. You must be careful when comparing data from 2 pie graphs.

28. Pie graph LettersFrequencyAngle of pie 32360÷35x2=21 45360÷35 x 5=51 514144 6772 7551 8221

29. Pie graph

30. Pie Graph This also is an appropriate graph as it shows the relative numbers in each category. It does not give us a lot of specific information like how many were surveyed or how many had 8 letters in their name.

31. Box and Whisker plot The box and whisker plot is a picture of the 5-number summary and it shows us where the cut-off is for every quarter of the data. Again, the box and whisker plot does not tell us how many were in the sample just how the quarters were distributed.

32. Box and Whisker plot

33. This gives us a lot of information. The lowest and highest values. The median, upper and lower quartiles. We also get a sense of how the data is distributed.

34. Box and Whisker Plot Box and whisker plots can also be used to compare two sets of data.

35. Back to strawberry picking! Who would you employ?

36. Strawberry picking

37. Comparing CarolDilip Mean90.490.1 Median9499 Mode9995

38. Comparing CarolDilip Mean 90.490.1 Median 9499 Mode 9995 Carol has the higher mean. Dilip has the higher median. Carol has the higher mode.

39. Central tendency Which central tendency is more useful in measuring the punnets picked overall?

40. Comparing CarolDilip Range62108 Interquartile range 177.5 Lowest450 Highest107108

41. Comparing CarolDilip Range 62108 Interquar tile range 177.5 Lowest 450 Highest 107108 Carol has the lower range. Dilip has the lower interquartile range. Carol’s lowest value is higher than Dilip’s. Dilip’s highest value is higher than Carol’s.

42. Spread Which picker is more reliable?

43. Back to the data

44. Comparing using a picture

45. Box and whisker

46. Overall they both picked roughly the same number of punnets. Carol 1537 Dilip 1532

47. Box and whisker The long tails on the box and whisker plots suggest outliers (extreme values). 45 is a likely outlier for Carol and suggests she worked a half day. 0 suggests that Dilip did not work on one of the days which would have pulled his mean value down. 49 is also an outlier for Dilip suggesting he also worked half a day.

48. Box and whisker Dilip is more reliable as his spread as shown by the interquartile range is smaller. (This is presuming he doesn’t just take days off when he wants to.)

49. What not to do!!!

50. No! No! No!- this is not a good idea!

51. Axes need to be labelled. Colour distorts the graph. Lines also distort the graph- take a look at these.

52. Are the lines parallel?

53. Are these lines parallel?

55. Are the lines parallel?

57. This kind of graph gives us very little information.

58. Negatively skewed (unimodal)

59. Positively skewed

60. Symmetric

61. Uniform

62. Groupings (bimodal)

63. Outlier

64. Bi-variate data Looking for relationships between two variables.

65. Example Is there a relationship between the amount of study a person does and their test result?

66. Consider data on ‘hours of study’ vs ‘ test score’ HoursScoreHoursScoreHoursScore 185914541759 166717721676 227414631459 279019722989 156220583093 288910473096 187128852382 196025752635 228418632278 30981961

68. Relationship There is a positive linear relationship between the amount of study and the test score. This means that as the hours of study increases, we expect an increase in test score.