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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? 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

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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.

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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

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5 Discrete Frequency Table: Example

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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?

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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.

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9 Making a Frequency Distribution Table from a Survey

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

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

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

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

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

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15 Making a Dot Plot from a Survey4 Intro Stats Classes

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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.

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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

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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?

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19 Making a Frequency Table

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20 Results for 4 Intro Stat Classes

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Dot Plot of Hair Length for 4 Classes

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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.

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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

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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.

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25 % of Population over 65Data

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26 % of Population over 65Dot Plot

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27 % of Population over 65Data

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28 % of Population over 65Data

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29 Student Scores Basic AlgebraData

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30 Student Scores in Basic AlgebraFreq Table

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31 Student Scores in Basic AlgebraFreq Table

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32 Student Scores Basic AlgebraDot Plot

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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?

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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.

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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

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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

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37 Data: Number of Cell Phones in Your Household

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38 Frequency Table: Number of Cell Phones in Your Household

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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?

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40 Dot Plot: Number of Cell Phones in Your Household

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41 Frequency Table: Number of Cell Phones in Your Household

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42 Frequency Table: Number of Cell Phones in Your Household

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43 Frequency Table: Number of Cell Phones in Your Household

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44 Frequency Table: Number of Cell Phones in Your Household

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

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46 Dot Plot: Number of Cell Phones in Your Household

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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.

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48 Spending by Shoppers at SafewayData

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49 Spending by Shoppers at SafewayFrequency Table

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50 Spending by Shoppers at SafewayFrequency Table

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51 Spending by Shoppers at SafewayData

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52 Loss of WetlandsData

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53 Loss of WetlandsData

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54 Loss of WetlandsData

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55 Loss of WetlandsData

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56 Tree CircumferenceData

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57 Tree CircumferenceBlank Rel Frequency Table

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58 Tree CircumferenceFrequency Dist Table

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59 Temperatures in AlaskaData

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60 Temperatures in AlaskaFrequency Table

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61 Temperatures in AlaskaFrequency Table

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62 Temperatures in AlaskaDot Plot

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63 Super Bowl AttendanceData

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64 Super Bowl AttendanceFrequency Table

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65 Super Bowl AttendanceFrequency Table

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66 Super Bowl AttendanceDot Plot

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