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Plinko

Andrew’s plot of his winning values is shown below.

A dotplot displaying the results of Andrew's winning values. The horizontal axis is numbered $100, $500, $1000, $0, $10,000, $0, $1000, $500, and $100. There are five dots above $100, three dots above $500, eleven dots above $1000, sixteen dots above $0, thirty dots above $10,000, eighteen dots above $0, nine dots above $1000, four dots above $500 and two dots above $100.

Did your table resemble Andrew’s plot? The more times you play the game, the more your table will resemble Andrew’s plot.

Statistically speaking, the more trials that are conducted, the trials will average to the mean of the data. Let’s look at another example to make this idea more clear since the Plinko scale is not a mathematically correct scale.

andrew and khalidKhalid and Andrew decide to revisit data on the presidents of the United States since there are a large number of presidents in that data set. The boys decide to examine the ages of  the presidents at their first inauguration.



President

Age at Inauguration

1. G. Washington

57

2. J. Adams

61

3. T. Jefferson

57

4. J. Madison

57

5. J. Monroe

58

6. J. Q. Adams

57

7. A. Jackson

61

8. M. Van Buren

54

9. W. H. Harrison

68

10.J. Tyler

51

11.J. Polk

49

12. Z. Taylor

64

13. M. Fillmore

50

14. F. Pierce

48

15. J. Buchanan

65

16. A. Lincoln

52

17. A. Johnson

56

18. U. Grant

46

19. R. Hayes

54

20. J. Garfield

49

21. C. Arthur

51

22. G. Cleveland

47

23. B. Harrison

55

24. G. Cleveland

55

25. W. McKinley

54

26. T. Roosevelt

42

27. W. H. Taft

51

28. W. Wilson

56

29. W. Harding

55

30. C. Coolidge

51

31. H. Hoover

54

32. F. D. Roosevelt

51

33. H. Truman

60

34. D. Eisenhower

62

35. J. F. Kennedy

43

36. L. Johnson

55

37. R. Nixon

56

38. G. Ford

61

39. J Carter

52

40. R. Reagan

69

41. G. H. Bush

64

42. W. Clinton

46

43. G. W. Bush

54

44. B. Obama

47

Khalid and Andrew will be using their graphing calculator to generate a histogram. The steps that Khalid and Andrew  follow to construct a histogram using a graphing calculator are shown below.  Produce the same histogram on your graphing calculator by following the given directions.

  • Enter the data into your graphing calculator. Be sure to include President Obama.

A screenshot from the graphing calculator. Three data lists are displayed: L one, L two, and L three. List L one has the numbers 52, 69, 64, 46, 54 and 47 displayed. Lists L two and L three are empty.

  • Turn on the first STAT PLOT and select the histogram icon.

A screen shot from the graphing calculator. The Stat Plot menu is shown. All four plots are off. The screen shot from the graphing calculator displaying the menu options for the first Stat Plot. The stat plot is being turned on, the type selected is the histogram, the x list is L one.

  • Adjust the WINDOW as shown.

A screen shot from the graphing calculator. The Window menu is displayed. The x minimum is set at 36, the x maximum is set at 76. The x scale is set at two. The y minimum is set at 0. The y-maximum is set at ten. The y scale is set at one. X resolution is left at one.

  • GRAPH the histogram.

A screen shot from the graphing calculator. The resulting histogram from the data in L one is shown. The data is in an approximately normal bell curve.

 

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