Statistics for Business and Economics. Chapter 2: Secs 1, 2 Methods for Describing Sets of Data

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2 MyStatLab We will use this program to assign and grade homework, for computations (StatCrunch), and for its various multimedia tools such as its Java Applets. Today, Mr. Chris Delaney from Pearson Publishing will explain how you get registered into the MyStatLab system so that you can begin to do homework and take advantage of its learning aids. Tomorrow in recitation, hardcopy of the registration directions will be handed out.

3 Statistics for Business and Economics Chapter 2: Secs 1, 2 Methods for Describing Sets of

4 Contents Sec 2.1 Sec 2.2 Describing Qualitative (minimal read: pp ) Graphical Methods for Describing Quantitative (minimal read: pp )

5 2.1 Describing Qualitative MyStatLab Exercises 1, 2 (Due 9/11/13, 11:59 pm)

6 Key Terms A class is one of the categories into which qualitative data can be classified. The class frequency is the number of observations in the data set falling into a particular class. The class relative frequency is the class frequency divided by the total numbers of observations in the data set. The class percentage is the class relative frequency multiplied by 100.

7 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

8 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

9 Summary Table 1. Lists categories & number of elements in category 2. Obtained by tallying responses in category 3. May show frequencies (counts), % or both Row Is Category Major Count Accounting 130 Economics 20 Management 50 Total 200 Tally:

10 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

11 Frequency Bar Graph Percent Used Also Equal Bar Widths Bar Height Shows Frequency or % Zero Point 0 Acct. Econ. Mgmt. Major Vertical Bars for Qualitative Variables

12 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

13 Pie Chart 1. Shows breakdown of total quantity into categories 2. Useful for showing relative differences Econ. 10% 36 Majors Mgmt. 25% 3. Angle size (360 )(percent) Acct. 65% (360 ) (10%) = 36

14 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

15 Frequency Pareto Diagram Like a bar graph, but with the categories arranged by height in descending order from left to right. Percent Used Also Equal Bar Widths Bar Height Shows Frequency or % Zero Point 0 Acct. Mgmt. Econ. Major Vertical Bars for Qualitative Variables

16 Summary 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. Pie chart: The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency. Pareto diagram: 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.

17 Thinking Challenge You re an analyst for IRI. You want to show the market shares held by Web browsers in Construct a bar graph, pie chart, & Pareto diagram to describe the data. Browser Mkt. Share (%) Firefox 14 Internet Explorer 81 Safari 4 Others 1

18 Market Share (%) Bar Graph Solution* 100% 80% 60% 40% 20% 0% Firefox Internet Explorer Safari Others Browser

19 Pie Chart Solution* Market Share Firefox, 14% Safari, 4% Others, 1% Internet Explorer, 81%

20 Market Share (%) Pareto Diagram Solution* 100% 80% 60% 40% 20% 0% Internet Explorer Firefox Safari Others Browser

21 2.2 Graphical Methods for Describing Quantitative MyStatLab Exercises 18, 19, 20, 21 (Due 9/11/13, 11:59 pm)

22 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

23 Dot Plot 1. Horizontal axis is a scale for the quantitative variable, e.g., percent. 2. The numerical value of each measurement is located on the horizontal scale by a dot.

24 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

25 Stem-and-Leaf Display 1. Separate each observation into stem value and leaf value Stems are listed in order in a column Leaf value is placed in corresponding stem row to right of bar Ordered : 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

26 Stem-and-Leaf Display (Double Stems) 1. Separate each observation into stem value and leaf value. Here we use each stem digit twice to capture greater detail in the distribution of the data. For example, use one stem of value 2 to hold leaves from {0,1,2,3,4} and the other to hold leaves from {5, 6, 7, 8, 9} Ordered : 21, 24, 24, 26, 27, 27, 30, 32, 38,

27 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

28 Frequency Distribution Table Steps 1. Determine range 2. Select number of classes Usually between 5 & 15 inclusive 3. Compute class intervals (typically equal width) 4. Determine class boundaries (limits) 5. Compute class midpoints 6. Count observations & assign to classes

29 Frequency Distribution Table Example Raw : 24, 26, 24, 21, , 41, 32, 38 Class Midpoint Frequency Width Boundaries (Lower + Upper Boundaries) / 2

30 Relative Frequency & % Distribution Tables Relative Frequency Distribution Percentage Distribution Class Prop. Class %

31 Presentation Presentation Qualitative Quantitative Summary Table Dot Plot Stem-&-Leaf Display Frequency Distribution Bar Graph Pie Chart Pareto Diagram Histogram

32 Histogram Frequency Relative Frequency Percent Count Class Freq Bars Touch