1 - 1 © 1997 Prentice-Hall, Inc. Statistical Methods

1 - 2 © 1997 Prentice-Hall, Inc. Descriptive Statistics n Involves l Collecting data l Presenting data l Characterizing data n Purpose l Describe data

1 - 3 © 1997 Prentice-Hall, Inc. Inferential Statistics n Involves l Estimation l Hypothesis testing n Purpose l Make decisions about population characteristics Population?

1 - 4 © 1997 Prentice-Hall, Inc. n Population (universe) l All items of interest n Sample l Portion of population n Parameter l Summary measure about population n Statistic l Summary measure about sample Key Terms

1 - 5 © 1997 Prentice-Hall, Inc. Data Types

1 - 6 © 1997 Prentice-Hall, Inc. Data Type Examples n Numerical l Discrete s To how many magazines do you subscribe currently? ___ (Number) l Continuous s How tall are you? ___ (Inches) n Categorical s Do you own savings bonds? __ Yes __ No

1 - 7 © 1997 Prentice-Hall, Inc. How Are Data Measured? n Nominal scale n Ordinal scale n Interval scale n Ratio scale

1 - 8 © 1997 Prentice-Hall, Inc. Standard Notation

1 - 9 © 1997 Prentice-Hall, Inc. Numerical Data Properties Central Tendency (Location) Variation (Dispersion) Shape

© 1997 Prentice-Hall, Inc. Numerical Data Properties & Measures

© 1997 Prentice-Hall, Inc. Central Tendency

© 1997 Prentice-Hall, Inc. MeanMean n Measure of central tendency n Most common measure n Acts as ‘balance point’ n Affected by extreme values (‘outliers’) n Formula (sample mean):

© 1997 Prentice-Hall, Inc. MedianMedian n Measure of central tendency n Middle value in ordered sequence l If odd n, middle value of sequence l If even n, average of 2 middle values n Not affected by extreme values n Position of median in sequence

© 1997 Prentice-Hall, Inc. ModeMode n Measure of central tendency n Value that occurs most often n Not affected by extreme values n May be no mode or several modes n May be used for numerical & categorical data

© 1997 Prentice-Hall, Inc. QuartilesQuartiles n Measure of noncentral tendency n Split ordered data into 4 quarters 25%25%25%25% Q1Q1Q1Q1 Q2Q2Q2Q2 Q3Q3Q3Q3

© 1997 Prentice-Hall, Inc. Summary of Central Tendency

© 1997 Prentice-Hall, Inc. VariationVariation

© 1997 Prentice-Hall, Inc. RangeRange n Measure of dispersion n Difference between largest & smallest observations n Ignores how data are distributed

© 1997 Prentice-Hall, Inc. Interquartile Range n Measure of dispersion n Also called midspread n Spread in middle 50% n Not affected by extreme values n Formula:

© 1997 Prentice-Hall, Inc. Variance & Standard Deviation n Measures of dispersion n Most common measures n Consider how data are distributed Show variation about mean (  X or  ) Show variation about mean (  X or  )

© 1997 Prentice-Hall, Inc. DISPERSION ABOUT THE MEAN VarianceVariance s 2 =

© 1997 Prentice-Hall, Inc. DISPERSION ABOUT MEAN (cont.) Standard deviation (sd)Standard deviation (sd) s =

© 1997 Prentice-Hall, Inc. PROPERTIES OF THE STANDARD DEVIATION IN A NORMAL CURVE 1s68% 2s95% 3s99%

© 1997 Prentice-Hall, Inc. Summary of Variation Measures

© 1997 Prentice-Hall, Inc. ShapeShape

© 1997 Prentice-Hall, Inc. ShapeShape n Describes how data are distributed n Measures of shape l Skew: Symmetry

© 1997 Prentice-Hall, Inc. Box-and-Whisker Plot n Graphical display of data using 5-number summary

© 1997 Prentice-Hall, Inc. Shape & Box-and-Whisker Plot

© 1997 Prentice-Hall, Inc. ConclusionConclusion n Explained numerical data properties n Described summary measures l Central tendency l Variation l Shape n Analyzed numerical data using summary measures

© 1997 Prentice-Hall, Inc. This Class... n What was the most important thing you learned in class today? n What do you still have questions about? n How can today’s class be improved? Please take a moment to answer the following questions in writing: