Chapter 2 Descriptive Statistics

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Chapter 2Descriptive Statistics

• 2-1 Overview
• 2-2 Summarizing Data with FrequencyTables
• 2-3 Pictures of Data
• 2-4 Measures of Center
• 2-5 Measures of Variation
• 2-6 Measures of Position
• 2-7 Exploratory Data Analysis (EDA)

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2 -1 Overview

• Descriptive Statistics
• summarize or describe the important
  characteristics of a known set of population
  data
• Inferential Statistics
• use sample data to make inferences (or
  generalizations) about a population

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2-2 Summarizing Data With Frequency Tables

• Frequency Table
• lists classes (or categories) of values, along
  with frequencies of the number of values that
  fall into each class

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Table 2-1
Computer Ratings
2 2 5 1 2 6 3 3 4 2 4 0 5 7 7 5 6 6 8 10 7 2 2
10 5 8 2 5 4 2 6 2 6 1 7 2 7 2 3 8 1 5 2 5 2 14
2 2 6 3 1 7
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Table 2-3
Frequency Table of Computer Ratings
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• Construction of Frequency Tables
• Definitions

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Lower Class Limits

• are the smallest numbers that can actually
  belong to different classes

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Lower Class Limits

• are the smallest numbers that can actually
  belong to different classes

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Lower Class Limits

• are the smallest numbers that can actually
  belong to different classes

Lower Class Limits
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Upper Class Limits

• are the largest numbers that can actually
  belong to different classes

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Upper Class Limits

• are the largest numbers that can actually
  belong to different classes

Upper Class Limits
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Class Boundaries

• are the numbers used to separate classes, but
  without the gaps created by class limits

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Class Boundaries

• numbers separating classes

- 0.5 2.5 5.5 8.5 11.5 14.5
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Class Boundaries

• numbers separating classes

- 0.5 2.5 5.5 8.5 11.5 14.5
Class Boundaries
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Class Midpoints

• midpoints of the classes

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Class Midpoints

• midpoints of the classes

Class Midpoints
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Class Width

• the difference between two consecutive lower
  class limits

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Class Width

• is the difference between two consecutive
  lower class limits

Class Width
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Constructing A Frequency Table

• 1. Decide on the number of classes . (Usually
  5 to 20)
• 2. Calculate Class width.

High - Low
class width
number of classes

• 3. Select the first lower class limit. (Either
  the lowest score or slightly lower.)
• 4. Add the class width to the first LCL to get
  the second LCL. Add the width again to get the
  third LCL . . .
• 5. Fill in all class limits.
• Tally.
• Total.

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Lets Try two examples

• Scores on a Statistics Final Exam
• Weights of Plastic Discarded in One Week

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Scores on a Stat Final
of classes class width first LCL
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Scores on a Stat Final
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Weights of Plastic Discarded
of classes class width first LCL
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Weights of Plastic Discarded