1. The Frequency Table or Frequency Distribution Table
Frequency Tables
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The Frequency Table or Frequency Distribution Table
What is it? Not a graph itself, but a prelude
to an important statistical graph
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2. What do Frequency Tables List?
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What do Frequency Tables List?
A frequency distribution table for quantitative data lists, in table format, the following:
1. All classes of grouped data
2. Tallies of those classes
3. Frequencies of those classes
4. Relative frequencies of those classes
5. Grand total of # of classes, frequencies and relative frequencies
Categorical or Qualitative
Quantitative or Numerical
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3. Frequency Table to Histogram
Frequency Tables
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Frequency Table to Histogram
What do frequency tables enable statisticians to construct?
They enable construction of histograms
What do frequency tables enable statisticians to see?
They enable them to see how data naturally group into classes.
Categorical or Qualitative
Quantitative or Numerical
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4. Discrete Frequency Table: Example
Frequency Tables
Discrete Frequency Table: Example
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Suppose there are 2000 families in a small town and the distribution of children among them is as follows:
300 families have no children
400 families have 1 child
700 families have 2 children
300 families have 3 children
100 families have 4 children
100 families have 5 children
100 families have 6 children
Make a frequency table of the data
Categorical or Qualitative
Quantitative or Numerical
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5. Discrete Frequency Table: Example
Frequency Tables
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Discrete Frequency Table: Example
Categorical or Qualitative
Quantitative or Numerical
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6. Discrete Frequency Table: Example
Frequency Tables
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Discrete Frequency Table: Example
Categorical or Qualitative
Quantitative or Numerical
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7. Making a Frequency Distribution Table
Frequency Tables
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Making a Frequency Distribution Table
I want to survey my classes on the subject of SIBLINGS. I want students to tell me the number of siblings that they have.
The result will answer my question,
“What is the number of siblings for Intro Stats students in this period class?”
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8. Discrete Frequency Tables
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Discrete Frequency Tables
Each SIBLING represents a class of its own SIBLING is a __________ _________ variable and so it is possible to make classes of only one value, which we will do in our survey. This will be one of the few examples of a single number class that we will explore.
Categorical or Qualitative
Quantitative or Numerical
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9. Making a Frequency Distribution Table from a Survey
Frequency Tables
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Making a Frequency Distribution Table from a Survey
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10. Frequency Tables
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Making a Frequency Distribution Table from a Survey— Period 2 Intro Stats 10
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11. Frequency Tables
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Making a Frequency Distribution Table from a Survey— Period 3 Intro Stats 11
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12. Frequency Tables
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Making a Frequency Distribution Table from a Survey— Period 4 Intro Stats 12
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13. Frequency Tables
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Making a Frequency Distribution Table from a Survey— Period 5 Intro Stats 13
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14. Frequency Tables
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Making a Frequency Distribution Table from a Survey— 4 Intro Stats Classes 14
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15. Making a Dot Plot from a Survey—4 Intro Stats Classes
Frequency Tables
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Making a Dot Plot from a Survey—4 Intro Stats Classes 15
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16. Discrete vs. Continuous Frequency Tables
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Discrete vs. Continuous Frequency Tables
In the sibling survey, each sibling represented a class of its own Sibling is a __________ ________ variable and so it is possible to make classes of only one value However, most of the data we will be looking at will be of the continuous type The next in-class survey will be “hair length” to the nearest inch—Hair Length is a _________ _________variable and so Class widths will no longer be 1.
Categorical or Qualitative
Quantitative or Numerical
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17. Frequency Distribution Table Definitions
Frequency Tables
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Frequency Distribution Table Definitions
What is a class on a frequency table? One line on a frequency table Determine these 2 things about Classes before constructing any Frequency Distribution Table: 1. Determine the starting point of the first class 2. Determine class widths before tallying begins
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18. Making a Frequency Distribution Table
Frequency Tables
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Making a Frequency Distribution Table
I want to survey my classes on the subject of hair length. I want students to estimate the ‘average’ length of the hair on their heads. I want everyone to use the rulers available to measure their hair to the nearest 1”.
This will help me answer the question, “How long is the average hair on an Intro Stats student in This Class?”
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19. Making a Frequency Table
Frequency Tables
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Making a Frequency Table
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20. Results for 4 Intro Stat Classes
Frequency Tables
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Results for 4 Intro Stat Classes 20
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21. Dot Plot of Hair Length for 4 Classes
Frequency Tables
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Dot Plot of Hair Length for 4 Classes
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22. When to use a frequency table?
Frequency Tables
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When?
When to use a frequency table?
When quantitative variables take on so many values (in so great a range or spread) that a graph of a distribution is clearer if nearby values are grouped together, or simply
when you want to draw a histogram.
Categorical or Qualitative
Quantitative or Numerical
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23. Characteristics of the Classes in Frequency Table
Frequency Tables
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Characteristics of the Classes in Frequency Table
Data is put in classes—A class could be 1 number or more than 1 number
Every class represents the same variable
Classes are not overlapping
Classes all have the same width
Classes vary from 4 to 10, depending on the spread of observations in the data set
Categorical or Qualitative
Quantitative or Numerical
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24. Other Frequency Table Definitions
Frequency Tables
Other Frequency Table Definitions
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Class Width
A class width is a distance: the first entry on the second line of a frequency table MINUS the first entry on the first line of a frequency table
Consistency in Class Widths
Class widths must ALWAYS be consistent for all classes in a frequency table
Number of Classes
The count of the # of lines that have been filled in on a frequency table, including zeroes if they are between filled-in lines.
Categorical or Qualitative
Quantitative or Numerical
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25. % of Population over 65—Data

26. % of Population over 65—Dot Plot

27. % of Population over 65—Data

28. % of Population over 65—Data

29. Student Scores Basic Algebra—Data

30. Student Scores in Basic Algebra—Freq Table

31. Student Scores in Basic Algebra—Freq Table

32. Student Scores Basic Algebra—Dot Plot

33. The Number of Cell Phones in your Household
I want to survey my classes on the subject of CELL PHONES. I want students to tell me the number of operating cell phone that are located in their household, including cell phones for parents (both personal and work cell phones), siblings, etc.
The result will answer my question,
“What is the number of CELL PHONES for the household of Intro Stats students in this period class?”

34. Discrete vs. Continuous Frequency Tables
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Discrete vs. Continuous Frequency Tables
Today, we will conduct a survey in class, counting the number of cell phones per household. As you take notes, please think about how many cell phones are used in your household. Cell Phone is a ________ ________ variable, so it is possible to make classes of only one value.
Categorical or Qualitative
Quantitative or Numerical
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35. Inequalities are not required when class width is 1
Frequency Tables
The Conventions of Writing Classes for Frequency Tables with Discrete Quantitative Variables
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Rules or Conventions for Discrete Classes (such as cell phones & siblings):
Inequalities are not required when class width is 1
If class width is > 1, use the rules for continuous classes
Data may never fall into more than 1 class
Categorical or Qualitative
Quantitative or Numerical
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36. How to Write Classes for Discrete Quantitative Variables
Frequency Tables
How to Write Classes for Discrete Quantitative Variables
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Example
In a survey of cell phones in a family, each quantity could become its own class
Class A 0 cell phones
Class B 1 cell phone
Class C 2 cell phones
Or we could group this data into wider classes
Class A 0 ≤ x < 2 cell phones
Class B 2 ≤ x < 4 cell phones
Class C 4 ≤ x < 6 cell phones
Categorical or Qualitative
Quantitative or Numerical
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37. Data: Number of Cell Phones in Your Household37

38. Frequency Table: Number of Cell Phones in Your Household38

39. Discrete vs. Continuous Frequency Tables
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Discrete vs. Continuous Frequency Tables
What class width did you use? How many classes did you have? Did you need to use inequalities to describe the class?
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Quantitative or Numerical 39
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40. Dot Plot: Number of Cell Phones in Your Household40

41. Frequency Table: Number of Cell Phones in Your Household41

42. Frequency Table: Number of Cell Phones in Your Household42

43. Frequency Table: Number of Cell Phones in Your Household43

44. Frequency Table: Number of Cell Phones in Your Household44

45. Frequency Table: Number of Cell Phones in 4 Classes’ Households45

46. Dot Plot: Number of Cell Phones in Your Household46

47. Frequency Tables
The Conventions of Writing Classes for Frequency Tables with Continuous Quantitative Variables
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Rules or Conventions for Continuous Classes:
1. The first inequality ALWAYS is a less than or equal (≤) sign
2. The second inequality is always a less than sign (<)
3. An x is written in between the two signs
4. ‘x’ should be defined
5. Data may NEVER fall into more than one class
Example
In a hair length survey, our first class might be 0”≤x<3”
Next class might be 3”≤x<6”, etc.
Categorical or Qualitative
Quantitative or Numerical
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48. Spending by Shoppers at Safeway—Data

49. Spending by Shoppers at Safeway—Frequency Table

50. Spending by Shoppers at Safeway—Frequency Table

51. Spending by Shoppers at Safeway—Data51

52. Loss of Wetlands—Data 52

53. Loss of Wetlands—Data 53

54. Loss of Wetlands—Data 54

55. Loss of Wetlands—Data 55

56. Tree Circumference—Data56

57. Tree Circumference—Blank Rel Frequency Table57

58. Tree Circumference—Frequency Dist Table58

59. Temperatures in Alaska—Data59

60. Temperatures in Alaska—Frequency Table

61. Temperatures in Alaska—Frequency Table

62. Temperatures in Alaska—Dot Plot

63. Super Bowl Attendance—Data

64. Super Bowl Attendance—Frequency Table

65. Super Bowl Attendance—Frequency Table

66. Super Bowl Attendance—Dot Plot