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Sta220 - Statistics

Sta220 - Statistics. Mr. Smith Room 310 Class #3. Section 2.1-2.2. Lesson Objectives. You will be able to: Describe Qualitative Data with Graphs Describe Quantitative Data with Graphs. Objective 1. Describe Qualitative Data with Graphs. Describing Data.

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Sta220 - Statistics

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  1. Sta220 - Statistics Mr. Smith Room 310 Class #3

  2. Section 2.1-2.2

  3. Lesson Objectives You will be able to: • Describe Qualitative Data with Graphs • Describe Quantitative Data with Graphs

  4. Objective 1 • Describe Qualitative Data with Graphs

  5. Describing Data Two methods for describing data are presented in this chapter, one graphical and the other numerical.

  6. Qualitative data are nonnumerical in nature; thus, the value of a qualitative variable can only be classified into categories called classes.

  7. A qualitative variable with three classes (X, Y, and Z) is measured for each of 20 units randomly sampled from a target population. The data (observed class for each unit are as follows:

  8. TYPES OF GRAPHS Three of the most widely used graphical methods for describing qualitative data: bar graphs, pie chart, and Pareto Diagram.

  9. When using a bar graph, the categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, class relative frequency, or class percentage.

  10. Bar Graph

  11. Bar Chart Restaurant Complaints Frequency Bar Chart

  12. Pie Chart

  13. Pie Chart Restaurant Complaints

  14. Pareto diagram is a bar graph with the categories (classes) of the qualitative variable (i.e., the bars) arranged by height in descending order from left to right. The goal of the Pareto diagram is to make it easy to locate the “most important”categories – those with the largest frequencies.

  15. Pareto Diagram

  16. Some Bad/Misleading Graphs

  17. Misleading Graphs A survey was conducted to determine what food would be served at the French Club Party. Explain how the following graph is misleading.

  18. The ratio of the heights of bars within each category does not reflect the actual ratio. • There is an implied precision that is unrealistic. (To the penny really?) • The percentages are computed incorrectly. A doubling of costs is only 100% increase.

  19. Sta220 - Statistics Mr. Smith Room 310 Class #4

  20. Section 2.2-2.4

  21. Lesson Objectives You will be able to: • Describe Quantitative Data with Graphs • Use Summation Notation • Understanding Central Tendency

  22. Lesson Objective # 2: Describe Quantitative Data with Graphs

  23. Recall that quantitative data sets consist of data that are recorded on a meaningful numerical scale. To describe, summarize, and detect patterns in such data, we can use three graphical methods: dot plots, stem-and-leaf displays and histograms.

  24. Dot Plot When using a dot plot, the numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale. When data values repeat, the dots are placed above one another vertically. The dot plot condenses the data by grouping all value that are the same.

  25. Dot Plot

  26. Stem-and-Leaf The stem-and-leaf display condenses the data by grouping all data with the same stem. The possible stems are listed in order in a column. The leaf for each quantitative measurement in the data set is placed in the corresponding stem row. Leaves for observations with the same stem value are listed in increasing order horizontally.

  27. Decimal point is 1 digit(s) to the right of the colon. 5 : 69 6 : 4 6 : 59 7 : 013 7 : 678 8 : 022 8 : 56 9 : 1122 9 : 589

  28. Histogram When using a histogram, the possible numerical values of the quantitative variable are partitioned into class intervals, each of which has the same width. These intervals form the scale of the horizontal axis. A vertical bar is placed over each class interval, with the height of the bar equal to either the class frequency or class relative frequency. When constructing histograms, use more classes as the number of values in the data set gets larger.

  29. Lesson Objective # 3: Use Summation Notation

  30. = 5 +1 + 3 + 2 + 1 = 12

  31. Lesson Objective # 4: Understanding Central Tendency

  32. The central tendency of the set of measurements – that is, the tendency of the data to cluster, or center, about certain numerical values The variability of the set of measurements – that is, the spread of the data.

  33. There are three measures of central tendency: mean, median and mode.

  34. MEAN

  35. MEDIAN • The median of a quantitative data is the middle number when the measurements are arranged in ascending (or descending) order.

  36. Calculating a Sample Median Μ Arrange the n measurements from the smallest to the largest. • If n is odd, Μ is the middle number. • If n is even, Μ is the mean of the middle two numbers. NOTE: Remember to order the data before calculating a value for the median

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