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Understanding and Creating Histograms: Key Concepts in Data Distribution

In this lecture by Professor Hao Wang from the University of South Carolina, students learn about the distribution of variables, focusing on categorical and quantitative data. The session highlights how to display data distributions using histograms, including steps for constructing them from a sample data set of test scores. Key concepts include determining ranges, class divisions, and the importance of class selection to accurately represent data shapes, avoiding the "skyscraper" and "pancake" effects in histogram presentation.

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Understanding and Creating Histograms: Key Concepts in Data Distribution

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  1. STAT 110 - Section 5 Lecture 13 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. Last time • Categorical and quantitative variables • The DISTRIBUTION of a variable tells us what values it takes and how often it takes these values. A distribution can be described by a table, graph, list, or function

  3. Last time

  4. Chapter 11 – Displaying Distributions with Graphs Histograms are the most common graph used to display the distribution of a quantitative variable.

  5. How to Make a Histogram • Divide the range of the data into classes of equal width. • Count the number of individuals in each class. • Draw the histogram.

  6. Histograms • Example • Let’s consider test scores.88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93 • What’s the range? • So, how should we divide the range into classes? • How many of the scores belong in each class? • Draw the histogram.

  7. Histograms 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93

  8. Histograms • You must use your judgment in choosing classes to display the shape of the data. • Too few classes will give a “skyscraper” effect, with all values in a few classes with tall bars. • Too many classes will give a “pancake” effect, with most classes having one or no observation. • The left endpoints of the bars are included, the right aren’t.

  9. A Sample Data Set

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