Probability and Statistics. Chapter 1

Transcription

1 Probability and Statistics Chapter 1

2 Individuals and Variables

3 Individuals and Variables Individuals are objects described by data.

4 Individuals and Variables Individuals are objects described by data. People

5 Individuals and Variables Individuals are objects described by data. People Animals

6 Individuals and Variables Individuals are objects described by data. People Animals Things

7 Individuals and Variables Individuals are objects described by data. People Animals Things A Variable is any characteristic of an individual

8 Individuals and Variables Individuals are objects described by data. People Animals Things A Variable is any characteristic of an individual Hair Color

9 Individuals and Variables Individuals are objects described by data. People Animals Things A Variable is any characteristic of an individual Hair Color Number of stripes

10 Individuals and Variables Individuals are objects described by data. People Animals Things A Variable is any characteristic of an individual Hair Color Number of stripes Number of Wheels

11 Categorical Variables

12 Categorical Variables A categorical Variable places an individual into one of several groups or categories

13 Categorical Variables A categorical Variable places an individual into one of several groups or categories Being a Freshman, Sophomore, Junior or Senior is a categorical variable

14 Categorical Variables A categorical Variable places an individual into one of several groups or categories Being a Freshman, Sophomore, Junior or Senior is a categorical variable It would be difficult to do arithmetic operations on categorical variables

15 Categorical Variables A categorical Variable places an individual into one of several groups or categories Being a Freshman, Sophomore, Junior or Senior is a categorical variable It would be difficult to do arithmetic operations on categorical variables What would it mean to add Freshman and Sophomores?

16 Quantitative Variables

17 Quantitative Variables A Quantitative Variable takes numerical values.

18 Quantitative Variables A Quantitative Variable takes numerical values. Arithmetical operations such as adding subtracting and averaging make sense.

19 Quantitative Variables A Quantitative Variable takes numerical values. Arithmetical operations such as adding subtracting and averaging make sense. The numbers of Freshman, Sophomores, Juniors and Seniors would be Quantitative variables

20 Quantitative Variables A Quantitative Variable takes numerical values. Arithmetical operations such as adding subtracting and averaging make sense. The numbers of Freshman, Sophomores, Juniors and Seniors would be Quantitative variables We could add them or subtract them

21 Quantitative Variables A Quantitative Variable takes numerical values. Arithmetical operations such as adding subtracting and averaging make sense. The numbers of Freshman, Sophomores, Juniors and Seniors would be Quantitative variables We could add them or subtract them We could average them

22 Do now!

23 Do now! Read p. 4-5

24 Do now! Read p. 4-5 Then answer the following!

25 Do now! Read p. 4-5 Then answer the following! p , 1.2

26 Distribution

27 Distribution The distribution of a variable tells us the range of values it takes and how often it takes these values.

28 Distribution The distribution of a variable tells us the range of values it takes and how often it takes these values. Pictures of Data depict the nature or shape of the data distribution

29 Bar Graphs vs. Pie Charts

30 Bar Graphs vs. Pie Charts Pie Charts are good for showing Categorical variables, but only if you have ALL of the categories.

31 Bar Graphs vs. Pie Charts Pie Charts are good for showing Categorical variables, but only if you have ALL of the categories. Bar Graphs can also show Categorical variables, but do not require ALL categories.

32 Pie Chart Firearms ( %) Ingestion of food or object ( % Motor vehicle (43, %) Fire ( %) Drowning ( %) Poison ( %) Accidental Deaths by Type Falls (12, %) 8

33 Bar Graphs vs. Pie Charts (cont.)

34 Bar Graphs vs. Pie Charts (cont.)!'#!%&!(#!%&!"#$%&!!#"%& )*+,-./0& *+,& 45062*,& 1+062*,&

35 Bar Graphs vs. Pie Charts (cont.)!'#!%&!(#!%&!"#$%&!!#"%& )*+,-./0& *+,& 45062*,& 1+062*,& +)#)%&!(#)%&!"#$%&!!#"%&!'#!%&!(#!%&!)#)%& *(#)%& *)#)%& (#)%& )#)%&,-./0123& /& /& /&

36 Bar Graphs vs. Pie Charts (cont.)!(#!%&!"#$%& )*+,-./0& *+,&!'#!%&!!#"%& 45062*,& 1+062*,& +)#)%&!(#)%&!"#$%&!!#"%&!'#!%&!(#!%&!'"'$%!'")$%!&"'$%!&"!$%!'"!$%!)#)%&!&")$% *(#)%&!*"'$%!*")$%!!"#$% *)#)%&!!"'$% (#)%&!!")$%!("'$% )#)%&,-./0123& /& /& /&!(")$% +,-.,/,012% 3456,02% +156,02%

37 Do now!

38 Do now! Read p.6-7

39 Do now! Read p.6-7 Then answer the following!

40 Do now! Read p.6-7 Then answer the following! p , 1.4

41 Histograms

42 Histograms A Histogram is a

43 Histograms A Histogram is a type of bar graph

44 Histograms A Histogram is a type of bar graph the horizontal axis often represents groups of data rather than individual datum

45 Histograms A Histogram is a type of bar graph the horizontal axis often represents groups of data rather than individual datum Choose the proper grouping of data for a good histogram

46 Histogram of Qwerty Word Ratings Rating Frequency Figure

47 Relative Frequency Histogram of Qwerty Word Ratings Rating Relative Frequency Figure % % % % % 13

48 Histogram and Relative Frequency Histogram Figure 2-2 Figure

49 Frequency Polygon 15

50 Histograms These six histograms each describe the same set of data from Table 1.2 on page 11 of your book. A B C '#" '!" &" '#" '!" %" &" $" %" #" $" #"!"!" '%('&" ')(#'" ##(#$" #*(#+" #&(,!",'(,," '%(#!" #'(#)" #%(*!" *'(*)" '&" '%" '$" %#" %!" $#" $!" #"!" $&'%(" %)'($" (%'(*" D E F +" *" (" %#" )" (" '" &" %" '" &" %" $" %!" $#" $!" $" #"!" #(,#)" #*,#+" $!,$#" $$,$%" $&,$'" $(,$)" $*,$+" %!,%#" %$,%%" #"!" #(" #)" #*" #+" $!" $#" $$" $%" $&" $'" $(" $)" $*" $+" %!" %#" %$" %%" #"!" $&'%(" %#'))"

51 Histograms These six histograms each describe the same set of data from Table 1.2 on page 11 of your book. A B C '#" '!" &" '#" '!" %" &" $" %" #" $" #"!"!" '%('&" ')(#'" ##(#$" #*(#+" #&(,!",'(,," '%(#!" #'(#)" #%(*!" *'(*)" '&" '%" '$" %#" %!" $#" $!" #"!" $&'%(" %)'($" (%'(*" D E F +" *" (" %#" )" (" '" &" %" '" &" %" $" %!" $#" $!" $" #"!" #(,#)" #*,#+" $!,$#" $$,$%" $&,$'" $(,$)" $*,$+" %!,%#" %$,%%" #"!" #(" #)" #*" #+" $!" $#" $$" $%" $&" $'" $(" $)" $*" $+" %!" %#" %$" %%" #"!" $&'%(" %#'))" Which one is most useful? least useful? Why?

52 DO NOW! Read p.8-11 Then answer the following! p

53 Interpreting Histograms Overall Pattern or Deviations from the Pattern Shape Center Spread Outlier(s)

54 Interpreting Histograms Overall Pattern or Deviations from the Pattern Shape Symmetrical or skewed, multiple peaks or single peak Center Spread Outlier(s)

55 Interpreting Histograms Overall Pattern or Deviations from the Pattern Shape Center Symmetrical or skewed, multiple peaks or single peak Roughly the value on the horizontal axis where half of the data are above the value and half of the data are below the value Spread Outlier(s)

56 Interpreting Histograms Overall Pattern or Deviations from the Pattern Shape Center Spread Symmetrical or skewed, multiple peaks or single peak Roughly the value on the horizontal axis where half of the data are above the value and half of the data are below the value Roughly the difference between the highest value and the lowest value, not including any outliers Outlier(s)

57 Interpreting Histograms Overall Pattern or Deviations from the Pattern Shape Center Spread Outlier(s) Symmetrical or skewed, multiple peaks or single peak Roughly the value on the horizontal axis where half of the data are above the value and half of the data are below the value Roughly the difference between the highest value and the lowest value, not including any outliers An individual value or values that lie well outside of the overall pattern

58 Symmetric vs. Skewed

59 Symmetric vs. Skewed #!" +" *" )" (" '" &" %" $" #"!"," -"." /" 0" 1" 2" 2" 3" Symmetrical

60 Symmetric vs. Skewed #!" +" *" )" (" '" &" %" $" #"!" #!" +" *" )" (" '" &" %" $" #"!"," -"." /" 0" 1" 2" 2" 3"," -"." /" 0" 1" 2" 2" 3" Symmetrical Skewed to the left

61 Symmetric vs. Skewed #!" +" *" )" (" '" &" %" $" #"!" #!" +" *" )" (" '" &" %" $" #"!"," -"." /" 0" 1" 2" 2" 3"," -"." /" 0" 1" 2" 2" 3" Symmetrical Skewed to the left '%" '$" '#" '!" &" %" $" #"!" (" )" *" +"," -"."." /" Skewed to the right

62 Do now!

63 Do now! Read p.11-14

64 Do now! Read p Then answer the following!

65 Do now! Read p Then answer the following! p

66 Do now! Read p Then answer the following! p click again

67 Do now! '#" Read p '!" &" Then answer the following! p %" $" #"!" '%('&" ')(#'" ##(#$" #*(#+" #&(,!",'(,," click again Histogram to use with 1.6

68 Stem Plots A plot similar to a Histogram. It consists usually of quantitative data. A Stem Plot (also sometimes called a Stem and Leaf Plot) consists of the data separated into the leaf (the right-most digit) and the stem (the remaining digits).

69 Stem Plots A plot similar to a Histogram. It consists usually of quantitative data. A Stem Plot (also sometimes called a Stem and Leaf Plot) consists of the data separated into the leaf (the right-most digit) and the stem (the remaining digits). Example: if using the numbers 15, 17, 23, 23, 25, 27, 27, 34, 36, 42 in a stem plot, we would use the tens digits as the stems and the ones digits as the leaves. You should also have a key that shows the reader what the stems and leaves represent.

70 Stem Plots (cont.) 15, 17, 23, 23, 25, 27, 27, 34, 36, 42

71 Stem Plots (cont.) 15, 17, 23, 23, 25, 27, 27, 34, 36, 42 Stem Leaves

72 Stem Plots (cont.) 15, 17, 23, 23, 25, 27, 27, 34, 36, 42 Stem Leaves Key 1 5 = 15

73 Stem Plots (cont. 2)

74 Stem Plots (cont. 2) You can choose the classes in a Stem Plot

75 Stem Plots (cont. 2) You can choose the classes in a Stem Plot Rounding

76 Stem Plots (cont. 2) You can choose the classes in a Stem Plot Rounding if your data is 1.453, 2.514, 2.534, 3.582, 3.617, 3.636, 4.644, 5.723, 5.742

77 Stem Plots (cont. 2) You can choose the classes in a Stem Plot Rounding if your data is 1.453, 2.514, 2.534, 3.582, 3.617, 3.636, 4.644, 5.723, you might want to round to 1.4, 2.5, 3.5, 3.6, 3.6, 4.6, 5.7, 5.7, then let the tenth be the leaves and the units be the stems

78 Stem Plot (cont. 3) 1.4, 2.5, 3.5, 3.6, 3.6, 4.6, 5.7, 5.7

79 Stem Plot (cont. 3) 1.4, 2.5, 3.5, 3.6, 3.6, 4.6, 5.7,

80 Stem Plot (cont. 3) 1.4, 2.5, 3.5, 3.6, 3.6, 4.6, 5.7, Key 1 4 = 1.4

81 Stem Plot (cont. 4) We can also split stems if the data would seem meaningless with a single stem.

82 Stem Plot (cont. 4) We can also split stems if the data would seem meaningless with a single stem

83 Stem Plot (cont. 4) We can also split stems if the data would seem meaningless with a single stem Key 2 1 = $2100

84 Stem Plot (cont. 5) Raw Data (Test Grades) Stem Leaves

85 DO NOW! Read p Then answer the following! p

86 Time Plot

87 Time Plot Measures observations relative to the time that they were observed.

88 Time Plot Measures observations relative to the time that they were observed. Time is always the independent variable (horizontal axis)

89 Time Plot Measures observations relative to the time that they were observed. Time is always the independent variable (horizontal axis) The observed variable is always the dependent variable (vertical axis)

90 Time Plot (Ex.) '$" *(+,-./0'607'8.#%' '#"!"#$%&'()'*(+,-./0' '!" &" %" $" #"!" 1%2&0'23%&'4555'

91 DO NOW! Read p Then answer the following! p

92 In Class Assignment Read Section 1.1 Summary p , 1.13, 1.14, , 1.25, 1.26