QM Spring 2002 Statistics for Decision Making Descriptive Statistics

Review  What is statistics? – Description (Data analysis) ---> Stage I – Inference (Applying results) ---> Stage 2  Data types – Quantitative (numeric) – Qualitative (categorical)  Introduction to descriptive analysis – Informal (tables & charts) – Summary measures

Schematic View

Sampling Population Sample Parameter Statistic

Very Important  Type of analysis depends upon data: – Quantitative Ratio Interval Ordinal – Qualitative Ordinal Nominal  Examples?

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

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

Primary Measures  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

Miscellaneous Statistics  Less important but need to be familiar with: – Location Median Mode Quantiles – Variation Range Min and Max – Both (?) Z-score Empirical Rule

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

Frequency Distributions Determining Frequency Groups  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 Frequencies  “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

Histograms  What are they? – Just graphical displays of frequency distributions Absolute frequencies Relative frequencies Cumulative frequencies – Provide “picture” of the variation in the data  Basics – Horizontal axis: values for variable of concern – Vertical axis: indicates corresponding frequencies

Qualitative Data: Charts & Tables  Frequency table is basis for chart Same as with numerical data, except data already are broken into frequency groups (categories)  Bar chart  Pie chart  Pareto chart

Bar Charts and Pie Charts  Bar chart – Two formats Vertical (preferred) Horizontal – Analogous to histograms, but Bars don’t touch each other Ordering of bars doesn’t matter  Pie chart – Often preferable to bar charts – Must identify slices

Summary  We’ve overviewed the basic informal means of describing data – Tables – Charts  Type of exhibit depends on data type – Quantitative – Qualitative  What’s next: numerical summary measures for numeric data