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Statistics 4

Statistics 4. This is an interesting bar graph. What does it tell us?. This is an interesting bar graph. What does it tell us?. We get an idea of how the temperature is changing in December. We also can see the daily ranges of temperature.

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Statistics 4

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  1. Statistics 4

  2. This is an interesting bar graph. What does it tell us?

  3. This is an interesting bar graph. What does it tell us? • We get an idea of how the temperature is changing in December. • We also can see the daily ranges of temperature.

  4. State whether the following data is discrete or continuous. • Number of books on library shelves • Lengths of library shelves • Time that the bells ring at a railway crossing • Weights of bales of wool • Number of bales of wool on trucks • Magnitude of earthquakes • Shoe size • Lengths of feet of year 9 boys

  5. State whether the following data is discrete or continuous. • Number of books on library shelves Discrete • Lengths of library shelves Continuous • Time that the bells ring at a railway crossing Continuous • Weights of bales of wool Continuous • Number of bales of wool on trucks Discrete • Magnitude of earthquakes Continuous • Shoe size Discrete • Lengths of feet of year 9 boys Continuous

  6. State whether the following data is discrete or continuous. • Number of pinetrees in plantations • Diameters of pinetrees in plantations • Weights of logs of wood • Number of times a telephone rings before it is picked up • Time a telephone rings before it is picked up • Lengths of songs in an album • Number of songs in an album

  7. State whether the following data is discrete or continuous. • Number of pinetrees in plantations Discrete • Diameters of pinetrees in plantations Continuous • Weights of logs of wood Continuous • Number of times a telephone rings before it is picked up Discrete • Time a telephone rings before it is picked up Continuous • Lengths of songs in an album Continuous • Number of songs in an album Discrete

  8. Looking at examples of Data and Graphs

  9. Example 1. Oil Consumption • The following chart was published by USA Today in June 1994

  10. Oil Consumption

  11. Oil Consumption • For what period of time is the fastest increase (either actual or projected) in world oil consumption shown? What is the rate of increase during this period?

  12. Oil Consumption If we check out the percentage increases: • 68.4/67.6 = 1.011= 1.1% • 75.6/68.4 = 1.105 = 10.5% • 81.3/75.6 = 1.075 = 7.5% • .. • Greatest increase was between 2000 and 2005.

  13. Oil Consumption Are you sure? Take another look at the x-axis scale.

  14. Are you sure? Take another look at the x-axis scale. Oil Consumption

  15. The scales were not even and hence our perspective is distorted. • The later figures represent 5 year periods.

  16. The greatest increase between 2000 and 2005 is represented by a yearly increase according to the equation 68.4 x (increase)5 = 75.6 Increase = 1.02 i.e. 2% per year This is still the greatest increase.

  17. Notice one more detail

  18. Notice one more detail • We haven’t reached 2010 yet!!!

  19. Stock Market • The Dow Jones Industrial Average (DJIA) is the best-known index measuring the rise and fall of the U.S. stock market. It is a weighted composite of the stock prices of 30 major companies. • The next chart, taken from a daily newspaper, shows the movement of the DJIA over a three-month period. Each bar represents one weekday (Monday through Friday), and dates are shown for every Monday. • The Boston Globe, June 21, 1994, p. 40.

  20. Stock Market

  21. Do you think this is the most appropriate graph?

  22. Example 3 • Maru works in a video store. For 60 consecutive days, he counted the number of videos that were hired. These were the figures he got:

  23. Example 3

  24. Data is discrete and hence a tally chart is the best way to organise this data.

  25. Organised data

  26. Appropriate graph

  27. Appropriate graph • Answer the questions on the sheet.

  28. Appropriate graph • In how days did Maru hire 34 videos? • 13 days

  29. Appropriate graph • In how days did Maru hire more than 34 videos? • 9 days

  30. Appropriate graph • In how days did Maru hire less than 34 videos? • 38 days

  31. Appropriate graph • What was the greatest number of videos hired? • 36

  32. Appropriate graph • What was the least number of videos hired? • 30

  33. Appropriate graph • Find the range (greatest minus least) of videos hired. • 36 - 30 = 6

  34. Appropriate graph • For this data find • The median • The mean • The mode

  35. Appropriate graph • For this data find • The median • =average of 30th and 31st data = 32 • The mean • Put it in the calculator to get 32.57 • The mode • The highest bar gives 34

  36. Complete question 2 for practice.

  37. Example 4 • For the following sets of data: • Pose a statistical question • Calculate the mean, median and mode for the data. (Central tendencies) • Calculate the range and interquartile range. (Measures of spread) • State what two graphs, in order of preference, you would draw to help answer your question.

  38. The following sets of maths marks are those obtained by a group of 7 formers in 2 different exams. The top row gives the mark in the term 3 school exam. The bottom row gives the mark in the Bursary exam.

  39. Question:Is there a relationship between the school exam result and the bursary result?

  40. Relationship questions don’t usually need us to calculate statistics as they have little meaning when we are finding a relationship.They are useful for comparing the results.

  41. Statistics

  42. Comments • Central tendencies: • Both the mean and median were higher in the school exam than in the bursary exam but the values were very close. • The mode has little meaning

  43. Comments • The range of bursary results was much smaller than the school results. This could be that those who had preformed very poorly had done some study.

  44. Comments • The interquartile range for bursary results was also smaller for the bursary exam.

  45. Comparing results

  46. Relationship graph School marks is considered the predictor variable and so it is put on the x-axis

  47. Appropriate graph

  48. Appropriate graph • We would conclude that there is a positive linear relationship between school marks and bursary marks I.e. as the school mark increases we generally expect an increase in bursary mark. • Note this doesn’t apply in all cases- it is a general observation.

  49. Example 5 • Measurements of the wrist width and forearm length of a group of young men provided the following data where both measurements are in mm.

  50. Question • We can’t really compare wrist and forearm data - it more of a relationship situation. • An appropriate question would be • “Is there a relationship between the wrist measurement and length of the forearm?”

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