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Grouping and Displaying Data to Convey Meaning:Tables and Graphs

Learning Objectives. 1.To show the difference between samples and populations2.To convert raw data into useful information3.To construct and use data arrays4. To construct and use frequency distributions5. To create histograms, polygons, and ogives6. To use frequency distributions to m

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Grouping and Displaying Data to Convey Meaning:Tables and Graphs

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    1. Grouping and Displaying Data to Convey Meaning:Tables and Graphs

    2. Learning Objectives 1. To show the difference between samples and populations 2. To convert raw data into useful information 3. To construct and use data arrays 4. To construct and use frequency distributions 5. To create histograms, polygons, and ogives 6. To use frequency distributions to make decisions As a result of this class, you will be able to...As a result of this class, you will be able to...

    3. Population vs. Sample

    4. Population vs. Sample

    5. Why Study Samples to Understand Population? 1) Easier than studying the whole population 2) Costs less 3) Takes less time 4) Sometimes testing involves risk 5) Sometimes testing requires the destruction of the item being studied

    6. Why Study Samples to Understand Population? 1) Easier than studying the whole population 2) Costs less 3) Takes less time 4) Sometimes testing involves risk 5) Sometimes testing requires the destruction of the item being studied

    7. Reliability of Data Ask the following questions: 1) What is the source of data? 2) Do the data support or contradict available evidence? 3) Is evidence missing that might cause us to come to a different conclusion? 4) What is the sample size? Does it represent the study group? 5) Is the conclusion logical and supported by data?

    8. Numerical Data Presentation

    9. Data Array 1. Organizes data to focus on major features 2. Data placed in rank order smallest to largest (or largest to smallest) 3. Data in raw form (as collected) 24, 26, 24, 21, 27, 27, 30, 41, 32, 38 4. Data in ordered array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

    10. Advantages/ Disadvantages of Data Array Advantages: o Quickly notice lowest and highest values in the data o Easily divide data into sections o Easily see values that occur frequently o Observe variability in the data Disadvantage: o Cumbersome

    11. Presenting Data in Array: An Example

    12. Presenting Data in Array: An Example

    13. Numerical Data Presentation

    14. Frequency Distribution What Is a frequency distribution? Table that organizes data into mutually exclusive classes Why called “frequency” distribution? Shows number of observations from data set that fall into each class What are the two classification schemes? Discrete classes Continuous classes

    15. Constructing an Ungrouped Frequency Distribution

    16. Constructing an Ungrouped Frequency Distribution

    17. Constructing an Ungrouped Frequency Distribution

    18. Constructing an Ungrouped Frequency Distribution

    19. Constructing an Ungrouped Frequency Distribution

    20. Steps in Constructing a Grouped Frequency Distribution 1. Determine the Class Interval Size Ideally, we wish to generate a frequency distribution with 10 class intervals. If this is not possible when following the next series of steps, then we would rather have more, but never fewer (i.e. less) than 10 class intervals. We would like the size (width) of each class interval to be in units of 1, 2, 3, 5, 10, 20, 30, 50, or multiples (factor of 10) of these values.

    21. Steps in Constructing a Grouped Frequency Distribution 1. Determine the Class Interval Size (continued) To Achieve These Goals, We Employ the Following Procedure:

    22. 1. Determine the Class Interval Size (continued) Example: Given the following data 100 74 84 95 95 110 99 87 100 108 85 103 99 83 91 91 84 110 113 105 100 98 100 108 100 98 100 107 79 86 123 107 87 105 88 85 99 101 93 99 R = 123 - 74 = 49 49/10 = 4.9 Tentative Class Interval Size = 5 Steps in Constructing a Grouped Frequency Distribution

    23. 2. Determine the Starting Point (First Class Interval) of the Frequency Distribution Start the Frequency Distribution with a Class Interval in Which the Following Guidelines Apply: The First Number of the Class Interval is a Multiple of the Class Interval Size. The First Interval Includes the Lowest Number or Value in the Data Set Steps in Constructing a Grouped Frequency Distribution

    24. Steps in Constructing a Grouped Frequency Distribution

    25. Additional Terms Associated with Grouped Frequency Distributions

    26. Numerical Data Presentation

    27. Histogram

    28. Numerical Data Presentation

    29. Frequency Polygon

    30. Frequency Polygon

    31. Frequency Polygon

    32. Numerical Data Presentation

    33. Ogive

    34. Creating Grouped Frequency Distributions and Graphic Illustrations with MVPStats

    35. Creating Grouped Frequency Distributions and Graphic Illustrations with MVPStats

    36. Creating Grouped Frequency Distributions and Graphic Illustrations with MVPStats

    37. Creating Grouped Frequency Distributions and Graphic Illustrations with MVPStats

    38. Conclusion 1. Explained the difference between samples and populations 2. Converted raw data into useful information 3. Constructed and used data arrays and frequency distributions 4. Created histograms and polygons using MVPStats

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