1. Box and Whisker Plots

2. 473021839463542 This data shows the scores achieved by fifteen students who took a short maths test. The test was marked out of ten. To construct a box and whisker plot, we need five pieces of information. The median The highest value The lowest value The upper quartile The lower quartile

3. To find the median and the upper and lower quartiles, we first of all need to arrange the data…. in rank order

4. 0

5. 01

6. 012

7. 0122

8. 01223

9. 012233

10. 0122333

11. 01223334

12. 012233344

13. 0122333444

14. 01223334445

15. 012233344456

16. 0122333444567

17. 01223334445678

18. 012233344456789

19. 012233344456789 The median value is the value where n is the number of data items, so here, n = 15. The median value is the8 th value which is 4

20. 012233344456789 The median value is the value where n is the number of data items, so here, n = 15. The median value is the8 th value which is 4 median

22. 012233344456789 The lower quartile is the value where n is the number of data items, so here, n = 15. The lower quartile is the4 th value which is 2 median

23. 012233344456789 The lower quartile is the value where n is the number of data items, so here, n = 15. The lower quartile is the4 th value which is 2 medianl.q.

25. 012233344456789 The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.

26. 012233344456789 The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.

27. 012233344456789 The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.u.q.

28. 012233344456789 medianl.q.u.q. The lowest value is 0

29. 012233344456789 medianl.q.u.q. The lowest value is 0 The highest value is 9

30. 012233344456789 medianl.q.u.q. The lowest value is 0 The highest value is 9

31. Now that we have found the median, both quartiles and the highest and lowest values, we have all the information which we need in order to be able to construct the box and whisker diagram

32. We first of all need some sort of grid. We can use graph paper for this or just ordinary squared paper will do equally well

33. 012233344456789 medianl.q.u.q. First of all we draw the box Data For this, we will need to provide a scale which should be clearly labelled

34. 012233344456789 medianl.q.u.q. 012345678910 Data Scores out of ten

35. 012233344456789 medianl.q.u.q. Next we draw the whiskers 012345678910 Data Scores out of ten

36. 012233344456789 012345678910 Data Scores out of ten

37. 012233344456789 The Box and Whisker Plot is complete 012345678910 Data Scores out of ten

38. 012233344456789 And the final diagram looks like this 012345678910 Data Scores out of ten

39. 012345678910 Scores out of ten

40. Box and Whisker plots are useful when comparing sets of data For instance, the scores of the original group of students, group A are now being compared with those of a second group B

41. Group A Group B Box and Whisker plots are useful when comparing sets of data For instance, the scores of the original group of students, group A are now being compared with those of a second group B 012345678910 Scores out of ten

42. Group A Group B 012345678910 Scores out of ten By simply examining the two side by side box and whisker plots, we can easily deduce lots of useful information. For instance………

43. Group A Group B The highest score was in group B 012345678910 Scores out of ten

44. Group A Group B The lowest score was in group A 012345678910 Scores out of ten

45. Group A Group B On average, group A did better 012345678910 Scores out of ten

46. Group A Group B The top 50% of students in group A did better than the bottom 75% of students in group B 012345678910 Scores out of ten

47. Group A Group B In group A, the middle 50% of the students scores were between 2 and 6 inclusive whereas with group B, the middle 50% of the students scores were contained in a narrower range of values between 2 and 4 inclusive. 012345678910 Scores out of ten

48. Group A Group B We could say a great deal more about these two diagrams 012345678910 Scores out of ten But now it’s your turn to draw and interpret some Box and Whisker diagrams of your own