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Chapter 3

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R
Rose Jenkins

This document provides an overview of key concepts in descriptive statistics including: - Parameters describe populations while statistics describe samples - Measures of central tendency include the mean, median, and mode - Measures of variation/dispersion include range, variance, standard deviation, and coefficient of variation - The empirical rule describes how many data points fall within a certain number of standard deviations from the mean for a normal distribution

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1 of 51
Chapter 3: Data Description
Parameter vs. Statistic ,[object Object],[object Object]
Parameter vs. Statistic ,[object Object],[object Object]
Measures of Central Tendency: Mean ,[object Object],[object Object],[object Object]
Measures of Central Tendency: Mean ,[object Object],[object Object]
Example: Chief Justices ,[object Object]
What Makes the Mean a Center? ,[object Object]
Measures of Central Tendency: Mean ,[object Object]
Measures of Central Tendency: Mean ,[object Object],[object Object]
Example: Mean Age of 120 Students ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Measures of Central Tendency: Median ,[object Object]
Example: Supreme Court Justices ,[object Object]
Example: Hospital System ,[object Object]
Measures of Central Tendency: Mode ,[object Object],[object Object],[object Object],[object Object]
Example: Birth Month Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Measures of Central Tendency: Mode ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Measures of Central Tendency: Midrange ,[object Object],[object Object]
Example: Midrange of Ages ,[object Object]
Measures of Central Tendency: Weighted Mean ,[object Object],[object Object]
Example: Weighted Mean ,[object Object]
Example: Weighted Mean ,[object Object]
Example: Weighted Mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
 
Measures of Variation 10.0 9.3 8.5 7.7 7.7 6.7 6.2 5.8 5.4 4.2 Bank of the USA 7.7 7.7 7.7 7.4 7.3 7.1 6.8 6.7 6.6 6.5 First Valley Bank Midrange Mode Median Mean Bank of the USA First Valley
Back-to-Back Stem & Leaf Plot First Valley Bank Bank of the USA 10.0 9.3 8.5 7.7 7.7 6.7 6.2 5.8 5.4 4.2 Bank of the USA 7.7 7.7 7.7 7.4 7.3 7.1 6.8 6.7 6.6 6.5 First Valley Bank
Range ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Measures of Variation Standard Deviation Range 75 75 75 75 Mean 90 77 0 75 80 76 100 75 70 74 100 75 60 73 100 75 Student D Student C Student B Student A
Deriving the Variation and Standard Deviation Formulas
Population Variance & Standard Deviation ,[object Object],[object Object],[object Object],[object Object]
Sample Variance & Standard Deviation ,[object Object],[object Object],[object Object],[object Object]
Example: ,[object Object],[object Object],[object Object],[object Object]
Finding the Standard Deviation From a Frequency Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Coefficient of Variation ,[object Object],[object Object]
Example ,[object Object]
Chebyshev’s Theorem ,[object Object],[object Object],[object Object]
Empirical Rule ,[object Object],[object Object],[object Object],[object Object]
 
Empirical Rule Example ,[object Object]
Example ,[object Object],[object Object]
Example ,[object Object],[object Object]
Example ,[object Object],[object Object]
Example ,[object Object],[object Object]
[object Object],[object Object]
[object Object]
Measures of Position ,[object Object],[object Object],[object Object]
[object Object]
Example ,[object Object]
Percentiles ,[object Object],[object Object],[object Object]
Find a Data Value Corresponding to a Given Percentile ,[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object]

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Chapter 3

  • 1. Chapter 3: Data Description
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.  
  • 24. Measures of Variation 10.0 9.3 8.5 7.7 7.7 6.7 6.2 5.8 5.4 4.2 Bank of the USA 7.7 7.7 7.7 7.4 7.3 7.1 6.8 6.7 6.6 6.5 First Valley Bank Midrange Mode Median Mean Bank of the USA First Valley
  • 25. Back-to-Back Stem & Leaf Plot First Valley Bank Bank of the USA 10.0 9.3 8.5 7.7 7.7 6.7 6.2 5.8 5.4 4.2 Bank of the USA 7.7 7.7 7.7 7.4 7.3 7.1 6.8 6.7 6.6 6.5 First Valley Bank
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  • 27. Measures of Variation Standard Deviation Range 75 75 75 75 Mean 90 77 0 75 80 76 100 75 70 74 100 75 60 73 100 75 Student D Student C Student B Student A
  • 28. Deriving the Variation and Standard Deviation Formulas
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