Statistics and Probability
Material Type:
Community College / Lower Division, College / Upper Division
Ohio Open Ed Collaborative
Box Plot, Center, Descriptive Statistics, Interquartile Range, Mean, Median, Spread, Standard Deviation
Creative Commons Attribution Non-Commercial
Media Formats:
Text/HTML, Video

Education Standards

Numerical Summary of Data


A data set is a listing of variables and their observed values on individuals or objects of study. In this topic we will learn about numerical summaries of data on a single variable and learn how to use them to describe data distribution and determine unusual values in the data. The type of numerical summaries to use depend on the data. We will also learn about boxplots.

Learning Objectives:

  • Understand which numerical summaries must be used to represent data
  • Be able to compute and interpret them. Also, know their properties and relative advantages and disadvantages. Further, use these measures to describe distributions, compare values from distributions, detect unusual values in the data, etc.
  • For categorical data use counts and proportions to describe categories
  • For quantitative data use
    • Measures of Center – Mean, Median, Mode
    • Measure of Spread – Range, Interquartile Range (IQR), Variance and Standard Deviation
    • Measures of Location – Minimum, Maximum, Quartiles and Percentiles
  • Learn to distinguish between different types of distributions for quantitative data – symmetric, skewed, bell-shaped, multimodal distributions
  • Learn about Empirical Rule for bell-shaped distributions
  • Use z-scores to compare values and detect unusual values
  • Make boxplot of data

Textbook Material: Chapter 2 – Descriptive Statistics – Pages 88 - 122

Suggested Homework
Chapter 2 - Descriptive Statistics – 29, 31, 32, 43, 57, 60, 69, 71, 82, 84, 86, 88, 89, 104, 106, 108, 109, 115, 119

Chapter 2 Exercises

Suggested Exercises - 

29, 31, 32, 43, 57, 60, 69,

71, 82, 84, 86, 88, 89,

104, 106, 108, 109, 115, 119

Chapter 2 - Exercises

Class Worksheet

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Descriptive Statistics Lab

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Key Terms

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