The Frequency Table or Frequency Distribution Table Frequency Tables 1 April 2017 1 April 2017 1 April 2017 The Frequency Table or Frequency Distribution Table What is it? Not a graph itself, but a prelude to an important statistical graph 12 Frequency Tables.ppt 1 1

What do Frequency Tables List? 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 2 2

Frequency Table to Histogram Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 3 3

Discrete Frequency Table: Example Frequency Tables Discrete Frequency Table: Example 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 4 4

Discrete Frequency Table: Example Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Discrete Frequency Table: Example Categorical or Qualitative Quantitative or Numerical 12 Frequency Tables.ppt 5 5

Discrete Frequency Table: Example Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Discrete Frequency Table: Example Categorical or Qualitative Quantitative or Numerical 12 Frequency Tables.ppt 6 6

Making a Frequency Distribution Table Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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?” 12 Frequency Tables.ppt 7 7

Discrete Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 8 8

Making a Frequency Distribution Table from a Survey Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey 12 Frequency Tables.ppt 9 9

Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey— Period 2 Intro Stats 10 12 Frequency Tables.ppt 10 10

Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey— Period 3 Intro Stats 11 12 Frequency Tables.ppt 11 11

Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey— Period 4 Intro Stats 12 12 Frequency Tables.ppt 12 12

Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey— Period 5 Intro Stats 13 12 Frequency Tables.ppt 13 13

Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Distribution Table from a Survey— 4 Intro Stats Classes 14 12 Frequency Tables.ppt 14 14

Making a Dot Plot from a Survey—4 Intro Stats Classes Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Dot Plot from a Survey—4 Intro Stats Classes 15 12 Frequency Tables.ppt 15 15

Discrete vs. Continuous Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 16 16

Frequency Distribution Table Definitions Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 17 17

Making a Frequency Distribution Table Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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?” 12 Frequency Tables.ppt 18 18

Making a Frequency Table Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Making a Frequency Table 12 Frequency Tables.ppt 19 19

Results for 4 Intro Stat Classes Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Results for 4 Intro Stat Classes 20 12 Frequency Tables.ppt 20 20

Dot Plot of Hair Length for 4 Classes Frequency Tables 1 April 2017 1 April 2017 1 April 2017 Dot Plot of Hair Length for 4 Classes 12 Frequency Tables.ppt 21 21

When to use a frequency table? Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 22 22

Characteristics of the Classes in Frequency Table Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 23 23

Other Frequency Table Definitions Frequency Tables Other Frequency Table Definitions 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 24 24

% of Population over 65—Data

% of Population over 65—Dot Plot

% of Population over 65—Data

% of Population over 65—Data

Student Scores Basic Algebra—Data

Student Scores in Basic Algebra—Freq Table

Student Scores in Basic Algebra—Freq Table

Student Scores Basic Algebra—Dot Plot

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?”

Discrete vs. Continuous Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 34 34

Inequalities are not required when class width is 1 Frequency Tables The Conventions of Writing Classes for Frequency Tables with Discrete Quantitative Variables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 35 35

How to Write Classes for Discrete Quantitative Variables Frequency Tables How to Write Classes for Discrete Quantitative Variables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 36 36

Data: Number of Cell Phones in Your Household 37

Frequency Table: Number of Cell Phones in Your Household 38

Discrete vs. Continuous Frequency Tables 1 April 2017 1 April 2017 1 April 2017 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? Categorical or Qualitative Quantitative or Numerical 39 12 Frequency Tables.ppt 39 39

Dot Plot: Number of Cell Phones in Your Household 40

Frequency Table: Number of Cell Phones in Your Household 41

Frequency Table: Number of Cell Phones in Your Household 42

Frequency Table: Number of Cell Phones in Your Household 43

Frequency Table: Number of Cell Phones in Your Household 44

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

Dot Plot: Number of Cell Phones in Your Household 46

Frequency Tables The Conventions of Writing Classes for Frequency Tables with Continuous Quantitative Variables 1 April 2017 1 April 2017 1 April 2017 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 12 Frequency Tables.ppt 47 47

Spending by Shoppers at Safeway—Data

Spending by Shoppers at Safeway—Frequency Table

Spending by Shoppers at Safeway—Frequency Table

Spending by Shoppers at Safeway—Data 51

Loss of Wetlands—Data 52

Loss of Wetlands—Data 53

Loss of Wetlands—Data 54

Loss of Wetlands—Data 55

Tree Circumference—Data 56

Tree Circumference—Blank Rel Frequency Table 57

Tree Circumference—Frequency Dist Table 58

Temperatures in Alaska—Data 59

Temperatures in Alaska—Frequency Table

Temperatures in Alaska—Frequency Table

Temperatures in Alaska—Dot Plot

Super Bowl Attendance—Data

Super Bowl Attendance—Frequency Table

Super Bowl Attendance—Frequency Table

Super Bowl Attendance—Dot Plot