2. Statistics for Decision Making Descriptive Statistics QM 2113 -- Fall 2003 Instructor: John Seydel, Ph.D.

3. Student Objectives Locate course materials Summarize course concepts Distinguish between the two primary types of data Summarize typical descriptive measures used for the different data types Perform basic descriptive statistics calculations Create visual summaries of univariate data

4. Let’s Start With a Case Read the Web Analytics caseWeb Analytics Let’s look at the revenue figures How much revenue does a website earn? Hard question to answer: there’s variability! But not all is lost; what’s a reasonable to answer the first question? Yes, the average! But...

5. Dealing With the Variation We can’t (or at least shouldn’t) ignore that there are differences among those values Look at a different set of data: Same average (almost) But there’s a lot of difference! So, what can we say about the variation among the values? How about summarizing it with the range? A better figure: the standard deviation Essentially, it’s the average difference among the values Not so easy to calculate That’s why we have computers!

6. Boiling Down Many Numbers to a Few Thus we can typically use two values to summarize a set of data The average (i.e., the mean) The standard deviation Easy to calculate with Excel =AVERAGE() =STDEV() Can we do this with all data? Consider another collection of observations, different from but related to the first...

7. Let’s Look at the Business Models How are these data different than the revenue data? Yes, these aren’t numbers Instead, they’re categories OK, so how would we describe the business model used by these firms? Again, yes, percentages Now, can we summarize the variation? No... !

8. We Now Need to Summarize What We’ve Experienced There will always be variation, but we can still concisely describe large amounts of information What the values tend to be The variation among the values Two types of data Numeric (e.g., revenues) Categorical (e.g., business models) We can summarize numeric data according to General tendency (e.g., the average) How different they are (e.g., the standard deviation) But the best we can do with categorical data is to list the percentages by category The difference: information content

9. What is statistics? Description (Data analysis) ---> Stage 1 Inference (Applying results) ---> Stage 2Stage 2 Data types Numeric (aka “quantitative”) Categorical (aka “qualitative”) Descriptive analysis Informal (tables & charts) Summary measures Inference: we’ll get there in a few weeks Now, Let’s Do an Overview

10. Type of analysis depends upon data: Numeric; you’ll also see these terms  Ratio  Interval  Ordinal Categorical; you’ll also see these terms  Ordinal  Nominal Other examples? Very Important

11. Three general forms Informal  Tables  Charts Formal: numeric (i.e., statistics) Forms basis for performing inferential analyses Descriptive Analysis

12. Categorical data Percentages Analysis of proportions Numeric data Single numbers that summarize  Location (i.e., general tendencies)  Variation (i.e., how different the values are) Primary importance  Mean  Standard deviation Descriptive Statistics (Formal)

13. Mean -- just a simple average Add the values and divide by number of observations Standard deviation Average difference among the values Process:  Subtract the average from each value  Square each result  “Average” the squared results  Take the square root of that result Primary Measures

14. Less important but need to be familiar with: Location  Median  Mode  Quantiles Variation  Range  Min and Max Both (?)  Z-score  Empirical Rule We’ll revisit these in a week or so Miscellaneous Statistics

15. Getting organized: Ordered array Frequency distribution  Absolute frequencies  Relative frequencies (%)  Cumulative frequencies Cumulative relative frequencies Histogram (frequencies) Other Stem-leaf display Ogive (cumulative frequencies) Numeric Data: Charts & Tables

16. Start by breaking the data range into k equal width intervals Let n represent the number of observations Number of intervals such that 2 k > n Interval width Start with: (Max - Min) / k Use convenient breakpoints for intervals  91.0 through 97.4 (OK)  90.0 through 95.0 (Better) Intervals: no overlap; no gaps Frequency Distributions: Determining Frequency Groups

17. “Absolute” frequencies Count number of observations in each interval Relative frequencies Divide absolute frequency by total number of observations Cumulative frequencies Add frequencies for all previous intervals (note difference from manner done in text) Cumulative relative frequencies Add relative frequencies for all previous intervals Frequency Distributions: Determining Frequencies

18. What are they? Just graphical displays of frequency distributions: absolute, relative, cumulative Provide “picture” of the variation in the data What they are not: Bar charts But they do for numeric data what bar charts do for categorical data Basics Horizontal axis: values for variable of concern Vertical axis: indicates corresponding frequencies Histograms

19. What is statistics all about? It’s about dealing with variation Summarizing information (description) Making decisions based upon that summarization Type of analysis depends on data type Numeric Categorical Description Formal  Numeric data: average and standard deviaiton  Categorical data: percentages Informal: frequency tables and charts data Summary

20. Appendix

21. Sampling Population Sample Parameter Statistic

22. Schematic View