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Welcome to Chapter 2 MBA 541

Welcome to Chapter 2 MBA 541. B ENEDICTINE U NIVERSITY Statistics and Frequency Distributions Describing Data: Frequency Distributions and Graphic Presentation Chapter 2. Chapter Two. Please, Read Chapter Two in Lind before viewing this presentation. Statistical Techniques in

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Welcome to Chapter 2 MBA 541

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  1. Welcome to Chapter 2MBA 541 BENEDICTINEUNIVERSITY • Statistics and Frequency Distributions • Describing Data: Frequency Distributions and Graphic Presentation • Chapter 2

  2. Chapter Two Please, Read Chapter Two in Lind before viewing this presentation. Statistical Techniques in Business & Economics Lind

  3. Goals When you have completed this chapter, you will be able to: • ONE • Organize data into a frequency distribution. • TWO • Portray a frequency distribution in a histogram, frequency polygon, and cumulative frequency polygon. • THREE • Present data using such graphic techniques as line charts, bar charts, and pie charts.

  4. Frequency Distribution A Frequency Distribution is a grouping of data into mutually exclusive categories showing the number of observations in each class.

  5. Constructing a Frequency Distribution Constructing a frequency distribution involves: • Determining the question to be addressed

  6. Constructing a Frequency Distribution Constructing a frequency distribution involves: • Determining the question to be addressed • Collecting raw data

  7. Constructing a Frequency Distribution Constructing a frequency distribution involves: • Determining the question to be addressed • Collecting raw data • Organizing data (frequency distribution)

  8. Constructing a Frequency Distribution Constructing a frequency distribution involves: • Determining the question to be addressed • Collecting raw data • Organizing data (frequency distribution) • Presenting data (graph)

  9. Constructing a Frequency Distribution Constructing a frequency distribution involves: • Determining the question to be addressed • Collecting raw data • Organizing data (frequency distribution) • Presenting data (graph) • Drawing conclusions

  10. A Simple Example of Creating a Frequency Distribution • The next few slides illustrate the steps in constructing a frequency distribution. • As Example 1, this illustrates, clarifies, and demonstrates the conceptual steps that were just discussed.

  11. A Simple Example of Creating a Frequency Distribution Background Information: • This company employs 17 individuals. • This company maintains employee records. • The company wants to understand employee length of service data.

  12. A Simple Example of Creating a Frequency Distribution Step 1: Determine the question to be addressed • An employer wants to answer the question, “How many people have worked for how many years at this business?”

  13. A Simple Example of Creating a Frequency Distribution Step 2: Collect the raw data.

  14. A Simple Example of Creating a Frequency Distribution Step 3: Determine the class interval or width. Here we will choose five classes with an interval of two years.

  15. A Simple Example of Creating a Frequency Distribution Step 4: Tally the results into classes.

  16. A Simple Example of Creating a Frequency Distribution Step 5: Present data (graph).

  17. A Simple Example of Creating a Frequency Distribution Step 6: Draw conclusions. • The majority of the employees have between 3 and 6 years of service. • Only one employee has more than 8 years of service.

  18. Definitions Class Interval:The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. The class intervals should be equal. Class Midpoint: A point that divides a class into two equal parts. This is the average of the upper and lower class limits. Class Frequency:The number of observations in each class.

  19. Example 2 Background: Dr. Tillman is Dean of the School of Business at Socastee University. He wishes to prepare a report showing the number of hours per week that students spend studying. He selects a random sample of 30 students and determines the number of hours that each student studied last week.

  20. Example 2 Step One: Decide on the number of class using the formula: Where: k = number of classes, and n = number of observations. • There are 30 observations so n = 30. • Two raised to the fifth power is 32. • Therefore, we should have at least 5 classes; i.e., k = 5.

  21. Example 2 Step Two: Determine the class interval or width by using the formula: Where: H = highest value, and L = lowest value. • Round up for an interval of 5 hours. • Set the lower limit of the first class at 7.5 hours. • Generate a total of 6 classes.

  22. Example 2 Step Three: Set the individual class limits and Steps Four and Five:Tally and count the number of items in each class.

  23. Example 2 Class Midpoint: find the midpoint of each interval by using the following formula:

  24. Example 2 – Chart 2-1

  25. Example 2 A Relative Frequency Distribution shows the percent of observations in each class.

  26. Graphic Presentations of a Frequency Distribution A Histogram is a graph on which the class midpoints or limits are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other. The three commonly used graphic forms are Histograms, Frequency Polygons, and Cumulative Frequency Polygons.

  27. Histogram For Hours Spent Studying midpoint

  28. Graphic Presentations of a Frequency Distribution A Frequency Polygon consists of line segments connecting the points formed by the class midpoints and the class frequency. The three commonly used graphic forms are Histograms, Frequency Polygons, and Cumulative Frequency Polygons.

  29. Frequency Polygon For Hours Spent Studying

  30. Graphic Presentations of a Frequency Distribution A CumulativeFrequency Polygon is used to determine how many or what proportion of the data values are below or above a certain value. To create a cumulative frequency polygon, scale the upper limit of each class along the X-axis and the corresponding cumulative frequencies along the Y-axis. The three commonly used graphic forms are Histograms, Frequency Polygons, and Cumulative Frequency Polygons.

  31. Cumulative Frequency TableFor Hours Spent Studying

  32. Cumulative Frequency Polygon For Hours Spent Studying

  33. Line Graphs Line graphs are typically used to show the change or trend in a variable over time.

  34. Example 3 - Line Graphs

  35. Example 3 – Chart 2-2

  36. Bar Chart A Bar Chart can be used to depict any of the levels of measurement: nominal, ordinal, interval or ratio.

  37. Bar Chart For the Unemployment Data

  38. Example 4 – Chart 2-3

  39. Pie Chart A Pie Chartis useful for displaying a relative frequency distribution. A circle is divided proportionally to the relative frequency and portions of the circle are allocated for the different groups. A sample of 200 runners were asked to indicate their favorite type of running shoe. Draw a pie chart based on the following information.

  40. Pie Chart For Running Shoes

  41. Example 5 – Chart 2-4

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