Data Summaries. Summary Statistics Given a large set of numbers, we often want to describe, or summarize, the data with a few revealing numbers. Example:

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Data Summaries

Summary Statistics Given a large set of numbers, we often want to describe, or summarize, the data with a few revealing numbers. Example: Yearly sales of two brands of peanut butter

Summary Statistics Given a large set of numbers, we often want to describe, or summarize, the data with a few revealing numbers. Example: Yearly sales of two brands of peanut butter

Summary Statistics Example: Yearly sales of two brands of peanut butter Measurements of Center Arithmetic Mean: The Average Median: The data point in the center

Summary Statistics Example: Yearly sales of two brands of peanut butter Skippy Mean: Jif Mean:

Summary Statistics Example: Yearly sales of two brands of peanut butter Median: Order the Data If even number average the two center numbers If odd number report the center number

Summary Statistics Example: Yearly sales of two brands of peanut butter Median: Order the Data If even number average the two center numbers If odd number report the center number two center numbers Skippy and Jif Median = 11

Why Use A Median? Example: Sales Force Compensation

Why Use A Median? Example: Sales Force Compensation

Why Use A Median? Example: Sales Force Compensation

Why Use A Median? Example: Sales Force Compensation

Summary Statistics Measurements of Variation Range: Largest - Smallest Standard Deviation: Square Root of Variance Variance: Average Squared Difference

Summary Statistics Example: Yearly sales of two brands of peanut butter Range: Largest - Smallest Skippy: Jif:

Summary Statistics Example: Yearly sales of two brands of peanut butter Variance: Average Squared Difference: Skippy Only

Summary Statistics Example: Yearly sales of two brands of peanut butter Variance: Average Squared Difference: Skippy Only

Summary Statistics Example: Yearly sales of two brands of peanut butter Variance: Average Squared Difference: Skippy Only

Summary Statistics Example: Yearly sales of two brands of peanut butter Standard Deviation: Square Root of Variance Skippy: Jif:

Graphical Summary A Picture is Worth a Thousand Words (Bar Chart)

Summary Statistics A Year Worth of Weekly Sales Figures

Summary Statistics Summary Statistics: Using SPSS Skippy Range = 16.94 - 4.56 = 12.38 Jif Range = 14.07 - 9.06 = 5.01

Graphical Summary Bar Chart

Graphical Summary Line Chart

Graphical Summary Histogram

Graphical Summary The Box and Whisker Plot

Antidepressant Survey Questionnaire Administered to 178 Physicians Randomly Selected from 100,000 physicians who prescribe of antidepressant drugs Investigating Physician Usage of Antidepressant medication

Questionnaire

Questionnaire

Summary Statistics Frequency Data (0/1 or 1 From Many)

Graphical Summary Pie Chart

Prescription Rates

Prozac Rates by Physician Type First, Box Plot Summaries by Physician Type Second, ReCode Data - High/Average /Low Prescription Rates

Prozac Rates by Physician Type Box Plot Summaries by Physician Type

Prozac Rates by Physician Type ReCode Data –Low Rate = 0 to 10 prescriptions per month –Average Rate = 10 to 20 prescriptions per month –High Rate = 20+ prescriptions per month

Cross Tabulating Data Create a Table Which Summarizes Number in Each Level

Graphing the Cross Tabulation Same Information Can be Summarized Using a Bar Plot

Next Class Period in Computer Lab Don’t forget: Next Period 11&14 BAB – from 7:15 p.m. to 9:00 p.m. We will not meet during the regularly class time during the day. Also, please bring a floppy disk to class, to save your work.

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