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An International Journal for Teachers |
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A List of Statistical
Investigations
Arthur Owen
(Torquay, England)
(From The Best of Teaching Statistics)
1. Estimate the proportion of black beads in a bag/ bottle from
(a) the distribution of the number of black beads in a sample of 10,
(b) the distribution of the number of beads which must be selected before
the first black one appears (or the fifth one, etc.).
2. As above, but this time estimate the number of white beads by first adding a known number of black ones. (This is known as the capture-recapture problem and it may be possible to use it to estimate the size of population of animals/ insects/fish by first marking a known number and then sampling.)
3 . How large must the above populations be if sampling without replacement is to give a good approximation to sampling with replacement? (Try it experimentally before/instead of working it out theoretically.)
4. Are there more draws in the Premier division than in the Third division of the English Football League?
5. Do Premier division teams score fewer goals than Third division teams? (Or English teams more than Scottish teams?)
6. Is there any relation between the number of goals scored by the home team and that scored by the away team?
7. Is there any relation between the number of points gained and the number of draws over a season?
8. Does a geiger counter show that radioactive particles are randomly distributed?
9. How random are random numbers tables? (Try occurrences of pairs of numbers as well as single numbers - and larger sequences if you have access to a computer.)
10. Can you obtain reliable random numbers from using a spinner, an icosahedral die, playing cards, or a telephone directory?
11. Do people arrive at supermarkets (or train stations, or post offices) randomly? What about cars at traffic lights?
12. Is it better in a post office to have a single queue which fills up the desks as they become free, or to have separate queues at each desk? (Try simulating the situation.)
13. Do school absences follow a random pattern or are some days of the week or weeks of the year or year groups of the school worse than others?
14. Do buses arrive at random? (Look at the gaps between arrivals.)
15. Do the number of 10p pieces in people's pockets follow a random pattern? Do boys have more than girls?
16. Do misprints in newspapers occur at random? Are some newspapers worse than others?
17. Do two authors vary (a) in their frequency of use of common words (b) in the lengths of sentences used?
18. Is the style of books written for younger pupils different from those for older pupils
19. Are people better at recalling sequences of letters or of words or of numbers? Are nonsense words of three letters harder to recall than proper words?
20. Is the variety of peas bought from one greengrocer the same as that from another, judging by the distribution of the number of peas in a pod?
21. As for 20, but with other vegetables or fruit using their "lengths" to compare two populations.
22. Estimate the proportion of left-handed people by finding the distribution of their frequency in samples of a given size. What confidence limits would you give?
23. Are males/mathematicians more likely than females/non-mathematicians to be left-handed?
24. Are left-handed people more clumsy than right-handed people? Devise a suitable test of dexterity to find out.
25. Estimate the proportion of foreign car users in the population from one or more samples. Give confidence limits for your estimate.
26. Does the number of cars passing in five minute intervals vary according to the time of day?
27. Try organising your own opinion poll on political or local matters. How accurate would a generalisation to a larger population be?
28. Put some woodlice in a cage in which one half is darkerldamper than the other. By taking counts of the numbers in each half at regular intervals decide which they prefer.
29. Compare the growth of mustard and cress seeds under different conditions, using either the percentage gerininating or the mean height.
30. Do plantains grow at random in the school field?
31. Is there any evidence from births announced in the Times/Telegraph that people (a) are more likely to announce the arrival of a boy (b) are likely to stop having children once they have a minimum of one of each sex?
32. Compare two makes of safety matches to see which stay lit longer.
33. By examining the distribution of the number of drawing pins falling point-up
in samples of size ten:
(a) Estimate the probability of any drawing pin of that type
falling point-up, giving confidence limits,
(b) Compare the shapes of two makes of drawing pins by comparing
the two distributions.
34. Estimate repeatedly the total number, N, of discs in a bag (numbered 1 to N) after drawing out discs one by one and noting the numbers so far. How many do you need to draw to be reasonably sure?
35. Is it likely that a number of marbles/dog biscuits/ nails/washers were all made on one machine? (Use a micrometer.)
36. Compare two labels of pop-records to see which gives the longer playing time.
37. How good a straight line do you get on physics experiments such as:
a) "period
of pendulum vs (length)"
b) or "extension of elastic
band vs measure recorded on forcemeter"?
38. Compare the grass/leaves in two different sites to see if there is any difference in mean length.
39. Does the distribution of dart-throws, when a dart is dropped onto a sheet of paper aiming at a central point, give a normal distribution? What difference does the height from which it is dropped make?
40. As for 39, but using grains of rice dropped on a point or a line.
41. Are pupils' homes randomly distributed around the school?
42. How good an estimate can you get of an area, volume, cost, etc. by getting a number of people to (a) estimate it (b) measure it.
43. Do you take longer to do a long multiplication when you are tired? Are 11 years olds faster than 16 year olds?
44. Do males have bigger heads/longer fingers than females?
45. Can you estimate standard deviation accurately using the range (or inter-quartile range)?
46. Is the median a "good" estimator of the mean? How good?
47. Do tall fathers produce tall children/have long fingers?
48. Do parents tend to give children a short first name if they have a long surname?
49. What relation is there between the score on one die and the total of it and the score on another die?
50. Is there a relation between ability at mathematics and a good memory/an
ear for music/big feet, etc.?
Acknowledgement
This is based upon a list in a booklet on Probability and Statistics
prepared by former HMI Arthur Owen, OBE.
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Please email: alison.davies2@ntu.ac.uk with any comments or corrections.
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The Teaching Statistics Trust 2006. The Teaching Statistics Trust is a registered
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ISSN 0141-982X (Print) ISSN 1467-9639 (Online)