1. Warm-Up: Believe It or Not?
A student claims that they have flipped a fair coin 200 times and only had 84 times the heads side of the coin showed up. Do you believe this student or not, discuss with your neighbor why or why not.

2. Chapters 2 - 4 The Role of Statistics & Graphical Methods for Describing Data

3. In order to learn Statistics, we need to learn the language of statistics first.
We’ll be learning a lot of new vocabulary today – through examples and activities

4. Statistics
the science of collecting, analyzing, and drawing conclusions from data

5. We could collect data from all high schools in the nation.
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from all high schools in the nation.
population

6. What term would be used to describe “all high school graduates”?
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from all high schools in the nation.
What term would be used to describe “all high school graduates”?
population

7. What do you call it when you collect data about the entire population?
The entire group of individuals or objects we want information about
A census attempts to contact every individual in the entire population
What do you call it when you collect data about the entire population?

8. Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from all high schools in the nation.

9. We could collect data from all high schools in the nation.
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from all high schools in the nation.
Why might we not want to use a census here?
If we didn’t perform a census, what would we do?

10. Sample
A part of the population that we actually examine in order to gather information
What would a sample of all high school graduates across the nation look like?
A list created by randomly selecting the GPAs of all high school graduates from each state.

11. We could collect data from a sample of high schools in the nation.
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from a sample of high schools in the nation.
Organize it – graph & make some calculations etc.

12. Once we have collected the data, what would we do with it?
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from a sample of high schools in the nation.
Organize it – graph & make some calculations etc.

13. Descriptive Statistics
the methods of organizing & summarizing data
If the sample of high school GPAs contained 10,000 numbers, how could the data be described or summarized?
Create a graph
State the range of GPAs
Calculate the average GPA

14. Could we use the data from this sample to answer our question?
Suppose we wanted to know something about the GPAs of high school graduates in the nation this year.
We could collect data from a sample of high schools in the nation.
Organize it – graph & make some calculations etc.
Could we use the data from this sample to answer our question?

15. Inferential statistics
involves making generalizations from a sample to a population
Be sure to sample from the population of interest!!

16. Inferential statistics
involves making generalizations from a sample to a population
Based on the sample, if the average GPA for high school graduates was 3.0, what generalization could be made?
The average national GPA for this year’s high school graduate is approximately 3.0.
Could someone claim that the average GPA for FISD graduates is 3.0?
No. Generalizations based on the results of a sample can only be made back to the population from which the sample came from.

17. Variable
any characteristic whose value may change from one individual or object to another

18. The number of wrecks per week at the intersection outside?
Variable
any characteristic whose value may change from one individual or object to another
Is this a variable . . .
The number of wrecks per week at the intersection outside?

19. Data
observations on a single variable or simultaneously on two or more variables

20. Data
observations on a single variable or simultaneously on two or more variables
For this variable . . .
The number of wrecks per week at the intersection outside what could the observations be?

21. Variability The range of possible data values
The goal of statistics is to understand the nature of variability in a population

22. Can you think of a population that has no variability?
The range of possible data values
The goal of statistics is to understand the nature of variability in a population
Populations with no variability are rare and boring (of little statistical interest).
Can you think of a population that has no variability?

23. Variability
The two histograms below display the distribution of heights of gymnasts and the distribution of heights of female basketball players. Which is which? Why?
Heights – Figure A
Heights – Figure B

24. Suppose you found a pair of size 6 shoes left outside the locker room
Suppose you found a pair of size 6 shoes left outside the locker room. Which team would you go to first to find the owner of the shoes? Why?
Suppose a tall woman (5 ft 11 in) you see is looking for her sister who is practicing in the gym. To which team would you send her? Why?
Center & spread

25. What aspects of the graphs helped you answer these questions?
Suppose you found a pair of size 6 shoes left outside the locker room. Which team would you go to first to find the owner of the shoes? Why?
Suppose a tall woman (5 ft 11 in) you see is looking for her sister who is practicing in the gym. To which team would you send her? Why?
Center & spread
What aspects of the graphs helped you answer these questions?

26. Types of variables

27. Categorical variables
(qualitative)
Variables where the possible values are set of categories

28. Numerical variables or quantitative
Variables where the values are numbers (are numerical)
(makes sense to average these values)
two types - discrete & continuous

29. Numerical: Discrete Values are isolated points on a number line
usually counts of items

30. Numerical: Continuous
Set of possible values form an entire interval on the number line
usually measurements of something

31. Classifying variables by the number of variables in a data set
Suppose that the PE coach records the height of each student in his class.
Univariate - data that describes a single characteristic of the population
This is an example of a univariate data

32. Classifying variables by the number of variables in a data set
Suppose that the PE coach records the height and weight of each student in his class.
Bivariate - data that describes two characteristics of the population
This is an example of a bivariate data

33. Classifying variables by the number of variables in a data set
Suppose that the PE coach records the height, weight, number of sit-ups, and number of push-ups for each student in his class.
Multivariate - data that describes more than two characteristics (beyond the scope of this course)
This is an example of a multivariate data

34. Identify the following variables:
the appraised value of homes in Faraway
the color of cars in the teacher’s lot
the number of calculators owned by students at your school
the zip code of an individual
the amount of time it takes students to drive to school
Continuous numerical
Categorical
Discrete numerical
Categorical
Continuous numerical

35. Warm-Up: Classifying variables
Write an example of a variable on the index card provided (try to come up with something we have not discussed in class already). Please include your name. When done, fold your index card in half and place in the bowl in the back of the room. We will classify these before completing notes on display types.

36. Graphs for categorical data

37. Bar Graph Used for categorical data Bars do not touch
Categorical variable is typically on the horizontal axis
Best used to describe or comment on which occurred the most often or least often
May make a double bar graph or segmented bar graph for bivariate categorical data sets

38. Comparative Bar Charts
Use relative frequency
If observations are the same for all groups (50 boys and 50 girls), you could use the frequency
Vertical scale the same
always label both axis
compare!!

39. Pie Chart (circle graph)
Used for categorical data
To make:
Proportion X 360°
Using a protractor, mark off each part
Best used to describe or comment on which occurred the most often or least often

40. Using class survey data, make bar graphs for: birth month gender & handedness
Since gender and handedness are two variables what ways could we display the data???
Stacked bar graph Use relative frequencies And same scales

41. Graphs for numerical data

42. Dotplot Used with numerical data (either discrete or continuous)
Made by putting dots (or X’s) on a number line
Can make comparative dotplots by using the same axis for multiple groups

43. Dotplot
To compare the weights of the males and females we put the dotplots on top of each other, using the same scales.

44. Using class survey data make dot plots of: # AP classes # siblings

45. Types (shapes) of Distributions

46. 1) Symmetrical
refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle
bell-shaped is a special type
has a center mound with two sloping tails

47. 2) Uniform
refers to data in which every class has equal or approximately equal frequency

48. 3) Skewed (left or right)
refers to data in which one side (tail) is longer than the other side
the direction of skewness is on the side of the longer tail

49. 4) Bimodal (multi-modal)
refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

50. Warm-Up: Example 1 (From Your Notes)
Looking at Example 1 (about sports-related injuries), complete the columns titled “Tally” and “Frequency”.

51. Graphical Methods for Describing Data

52. Frequency Distributions
The relative frequency for a particular category is the fraction or proportion of the time that the category appears in the data set. It is calculated as
When the table includes relative frequencies, it is sometimes referred to as a relative frequency distribution.

53. Example1 Category Tally Frequency Relative freq. Cum rel. freq Sprain
Contusion
Fracture
Strain
Laceration
Chronic
Dislocation
Concussion
Dental 13 12 14 6 3 2 1
.2321
.2321
13/56
.4464
.2143
12/56
.6964
.25
.8035
.8569
.8926
.946
.9817
1.00
.1071
.0534
.0357
.0179

54. Bar Chart – Example (frequency)
None
Glasses 31
Contacts 10 79

55. Bar Chart – (Relative Frequency)

56. Pie Chart
5% of 360 = 18
11% of 360 = 39.6

57. you drove 102 – put it next to 10
Class data: fastest speed you have ever driven. Take that speed and your gender and put it on a sticky note.
In a moment, you will place you sticky note next to the digit(s) that represent tenths on the white board. For example,
you drove 102 – put it next to 10
You drove 87 – put it by the 8
Build a stem plot and then convert to a comparative stemplot

58. Fastest speed driven 3 4 5 6 7 8 9 10 11 12 13
8│7 is 87 mph

59. Stemplots (stem & leaf plots)
Used with univariate, numerical data
Must have key so that we know how to read numbers

60. Stemplots (stem & leaf plots)
Used with univariate, numerical data
Must have key so that we know how to read numbers
Would a stemplot be a good graph for the number of pieces of gun chewed per day by Stat students? Why or why not?

61. Stemplots (stem & leaf plots)
Used with univariate, numerical data
Must have key so that we know how to read numbers
Can split stems when you have long list of leaves
Can have a comparative stemplot with two groups

62. Stemplots (stem & leaf plots)
Used with univariate, numerical data
Must have key so that we know how to read numbers
Can split stems when you have long list of leaves
Can have a comparative stemplot with two groups
Would a stemplot be a good graph for the number of pairs of shoes owned by AP Stat students? Why or why not?

63. Can you make a stemplot with this data?
Example 2:
The following data are price per ounce for various brands of dandruff shampoo at a local grocery store.
Can you make a stemplot with this data?
Do examples on separate note paper

64. Greed Example 3: Tobacco use in G-rated Movies
Total tobacco exposure time (in seconds) for Disney movies:
Total tobacco exposure time (in seconds) for other studios’ movies:
Make a comparative stemplot.
Greed

65. Dotplots Stem & leaf plots Histograms Boxplots
How to describe a graph
Dotplots
Stem & leaf plots
Histograms
Boxplots
Do after Features of Distributions Activity

66. 1. Center discuss where the middle of the data falls
three types of central tendency
mean, median, & mode

67. 2. Spread discuss how spread out the data is
refers to the variability of the data
Range, standard deviation, IQR

68. 3. Type of distribution
refers to the overall shape of the distribution
symmetrical, uniform, skewed, or bimodal

69. 4. Unusual occurrences
outliers - value that lies away from the rest of the data
gaps
clusters
anything else unusual

70. 5. In context
You must write your answer in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!

71. Histograms Used with numerical data Bars touch on histograms Two types
Discrete
Bars are centered over discrete values
Continuous
Bars cover a class (interval) of values
For comparative histograms – use two separate graphs with the same scale on the horizontal axis

72. Example 4 Height (inches) Tally Height (Inches) 62 1 69 10 63 3 70 6471 9 65 7 72 66 73 67 12 74 68 13 75

73. Cumulative Relative Frequency Plot (Ogive)
. . . is used to answer questions about percentiles.
Percentiles are the percent of individuals that are at or below a certain value.
Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2?
Interquartile Range (IQR) is the range of the middle half (50%) of the data.
IQR = Q3 – Q1
Ex. 4

74. Example 5 Notes

75. Relative Frequencies, Cumulative Frequencies, & Ogives

76. Review: Histograms Patterns
Center: for now, the value that divides the observations roughly in half
Spread (variability): the extent of the data from smallest to largest value
Shape: overall appearance of distribution
Outlier (Unusual): an individual observation that falls outside the overall pattern
CUSS

77. Let’s practice….
Can you describe the shape of the following distributions?

78. symmetrical
Frequency

79. slightly skewed left (negative skew)
Frequency

80. strongly skewed right (positive skew)
Frequency

81. bimodal
Frequency

82. skewed left with outlier
Frequency

83. bimodal
Frequency

84. strongly skewed left
Frequency

85. Guess Age
Guess the age of the person in the picture (do not discuss this with your partner, just write down your guess.)
After everyone has guessed, I will give you the actual ages.
Graph a scatter plot of Guess Age vs. Actual Age (Be sure to label the axes.)

86. A

87. B

88. C

89. D

90. E

91. F and G
how old is he?
how old is she?

92. H

93. COMPARE
A 27
B 38
C 8
D 115
E 22
F she’s 80, G he’s 90
H 19

94. Generate a scatterplot
What would you expect from these scatterplots?
If your guesses were accurate?
If you under estimated?
Over estimated?

95. Scatterplots
A scatterplot shows the relationship between two quantitative variables measured on the same individuals.
The explanatory variable, if there is one, is graphed on the x-axis.
Scatterplots reveal the direction, form, and strength.

96. Patterns
Direction: variables are either positively associated or negatively associated
Form: linear is preferred, but curves and clusters are significant
Strength: determined by how close the points in the scatterplot are linear
Note: A strong association does NOT indicate cause and effect!

97. Scatterplot Plot the data.
Math
Verbal
690
510
720
610
590
550
760
660
700
630
650
710
730
540
800
620
780
Plot the data.
Describe the relationship between the SAT Math and SAT Verbal scores

98. Time Plot (aka time-series plot)
This a plot of each observation against the time at which it was measured
Stock prices, sales figures, other socio-economic data
Invaluable for identifying trends
Y-variable, x-time when observation made
Used to plot trends or cycles