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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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Presentation on theme: "The Frequency Table or Frequency Distribution Table What is it? Not a graph itself, but a prelude to an important statistical graph."— Presentation transcript:

1 The Frequency Table or Frequency Distribution Table What is it? Not a graph itself, but a prelude to an important statistical graph

2 2 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

3 3 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.

4 4 Discrete Frequency Table: Example Suppose there are 2000 families in a small town and the distribution of children among them is as follows: 300 familieshave no children 400 familieshave 1 child 700 families have 2 children 300 families have 3 children 100 families have 4 children 100 families have 5 children 100 familieshave 6 children Make a frequency table of the data

5 5 Discrete Frequency Table: Example

6 6

7 7 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?

8 8 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.

9 9 Making a Frequency Distribution Table from a Survey

10 10 Making a Frequency Distribution Table from a Survey Period 2 Intro Stats

11 11 Making a Frequency Distribution Table from a Survey Period 3 Intro Stats

12 12 Making a Frequency Distribution Table from a Survey Period 4 Intro Stats

13 13 Making a Frequency Distribution Table from a Survey Period 5 Intro Stats

14 14 Making a Frequency Distribution Table from a Survey 4 Intro Stats Classes

15 15 Making a Dot Plot from a Survey4 Intro Stats Classes

16 16 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 inchHair Length is a _________ _________variable and so Class widths will no longer be 1.

17 17 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

18 18 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?

19 19 Making a Frequency Table

20 20 Results for 4 Intro Stat Classes

21 Dot Plot of Hair Length for 4 Classes

22 22 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.

23 23 Characteristics of the Classes in Frequency Table 1.Data is put in classesA class could be 1 number or more than 1 number 2.Every class represents the same variable 3.Classes are not overlapping 4.Classes all have the same width 5.Classes vary from 4 to 10, depending on the spread of observations in the data set

24 24 Other Frequency Table Definitions 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.

25 25 % of Population over 65Data

26 26 % of Population over 65Dot Plot

27 27 % of Population over 65Data

28 28 % of Population over 65Data

29 29 Student Scores Basic AlgebraData

30 30 Student Scores in Basic AlgebraFreq Table

31 31 Student Scores in Basic AlgebraFreq Table

32 32 Student Scores Basic AlgebraDot Plot

33 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 34 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.

35 35 The Conventions of Writing Classes for Frequency Tables with Discrete Quantitative Variables Rules or Conventions for Discrete Classes (such as cell phones & siblings): 1.Inequalities are not required when class width is 1 2.If class width is > 1, use the rules for continuous classes 3.Data may never fall into more than 1 class

36 36 How to Write Classes for Discrete Quantitative Variables 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 C2 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

37 37 Data: Number of Cell Phones in Your Household

38 38 Frequency Table: Number of Cell Phones in Your Household

39 39 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?

40 40 Dot Plot: Number of Cell Phones in Your Household

41 41 Frequency Table: Number of Cell Phones in Your Household

42 42 Frequency Table: Number of Cell Phones in Your Household

43 43 Frequency Table: Number of Cell Phones in Your Household

44 44 Frequency Table: Number of Cell Phones in Your Household

45 45 Frequency Table: Number of Cell Phones in 4 Classes Households

46 46 Dot Plot: Number of Cell Phones in Your Household

47 47 The Conventions of Writing Classes for Frequency Tables with Continuous Quantitative Variables 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 0x<3 Next class might be 3x<6, etc.

48 48 Spending by Shoppers at SafewayData

49 49 Spending by Shoppers at SafewayFrequency Table

50 50 Spending by Shoppers at SafewayFrequency Table

51 51 Spending by Shoppers at SafewayData

52 52 Loss of WetlandsData

53 53 Loss of WetlandsData

54 54 Loss of WetlandsData

55 55 Loss of WetlandsData

56 56 Tree CircumferenceData

57 57 Tree CircumferenceBlank Rel Frequency Table

58 58 Tree CircumferenceFrequency Dist Table

59 59 Temperatures in AlaskaData

60 60 Temperatures in AlaskaFrequency Table

61 61 Temperatures in AlaskaFrequency Table

62 62 Temperatures in AlaskaDot Plot

63 63 Super Bowl AttendanceData

64 64 Super Bowl AttendanceFrequency Table

65 65 Super Bowl AttendanceFrequency Table

66 66 Super Bowl AttendanceDot Plot


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