1. Chapter 2 Presenting Data in Tables and Charts

2. 2.1 Tables and Charts for Categorical Data Mutual Funds –Variables? Measurement scales? Four Techniques 1.The summary table 2.The bar chart 3.The pie chart 4.The Pareto Diagram (and Pareto Principle)

3. 2.2: Organizing Numerical Data Big tables of data are difficult to fit into our minds. Two basic techniques: 1.Ordered Array –For each variable, arrange the data points in order (lowest to highest, etc.). Table 2.5 shows unarranged. Table 2.6 shows arranged. Interpret.

4. 2.Stem and Leaf –For each variable, separate each data point into leading digits (stems) and trailing digits (leaves) –E.g. “49” = “4” for stem and “9” for leaf –Plot (smallest is on top) –Example on page 30 is awful (rounding). –Figure 2.7 awful. –Example 2.5 interpretation is quite good. –Our problem…

5. 2.3: Tables and Charts for Numerical Data Draw conclusions from a large set of data. Summarization. Frequency = the number of times something occurs. Frequency distribution = a presentation of frequencies where the data set has been arranged in groups or categories. The presentation may be a formula, a chart, a rule, or a table.

6. Frequency Distributions (FD) How many categories or groups, usually known as classes? How “wide” is each class, usually known as the class interval or class width? What are the boundaries of the classes?

7. FDs There will be many alternate ways to make a correct FD: judgment is required. # of class intervals: between 5 and 15. More data points means more intervals. Class width = data range / # of intervals (all class widths are equal). Formula 2.1, p 33. Class boundaries must not overlap. Use judicious rounding to make the data easy to work with and easy to interpret.

8. Text Example of FD n = 50 # of intervals = 10 Range = 63-14 = 49 Width = 49/10 = 4.9 or approximately 5 14 is approximately 10. 10+5 = 15. Etc. Result is Table 2.7. Notice side-by-side. Class Midpoint. Pick a different # of intervals if it improves FD.

9. Relative FD Relative and Percentage FDs are possible by dividing the frequency by the number of points in the data set. Often more intuitively useful than plain old frequencies. Very useful for comparing data sets. Requirements for comparison? Table 2.9, p 35.

10. Cumulative Distribution Table 2.11, p 36. Successive addition of frequencies or percentage frequencies. In other words, keep a running total of the number or percentage of the data points that have been used in the table.

11. Histogram Graphical version of a FD. Bar height (or bar length) represents the frequency or percentage frequency. Bar widths are equal. Variable of interest on the horizontal axis. See Figure 2.8, p 37.

12. Frequency Polygons Plot the frequencies or percentage frequencies (at the class midpoints) and connect with lines. The polygon is the shape created by this procedure. Variable of interest on the horizontal axis. Very useful for graphically comparing FDs. See Figure 2.10, p 39.

13. Cumulative Frequency Polygon “ogive” Same basic structure: –Variable values on the x-axis (use the class midpoints) –Cumulative frequencies or cumulative percentage frequencies on the y-axis. Y-axis should start at “0”. –Connect the points Best use is for comparing FDs of 2 or more variables.

14. 2.4 Cross Tabulations Cross-tab tables or contingency tables or cross-classification tables. Two or more CATEGORICAL variables. Pivot Table is your best friend. Tables 2.14 and 2.15 are the best. Don’t use Tables 2.16 and 2.17 in this class. “Chartify” in side-by-side chart.

15. 2.5 Scatter Diagrams and Time-Series Plots Scatter Diagram Two NUMERICAL variables. “… examine possible relationships….” anatomy of graphs and relationships Time-Series Plot Variable on X-axis or horizontal-axis is time.