Chapter 4 Introduction

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CHAPTER 4

Central Tendency and Variability

Central Tendency

Mean, the Arithmetic Average

Median, the Middle Score

Mode, the Most Common Score

How Outliers Affect Measures of Central Tendency

Which Measure of Central Tendency Is Best?

Measures of Variability

Range

Variance

Standard Deviation

BEFORE YOU GO ON

  • You should understand what a distribution is (Chapter 2).

  • You should be able to interpret histograms and frequency polygons (Chapter 2).

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Nagasaki, Two Days Before the Atomic Bomb
MPI/Getty Images
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Nagasaki, Three Days After the Atomic Bomb

Chance variability in the cloud cover diverted a B-29 bomber from Kokura, Japan, on August 9, 1945. The World War II bomber banked instead toward its secondary target, the city of Nagasaki. When the atomic bomb exploded a few hundred feet above a tennis court, all of the buildings and most of the people who lived in the city of Nagasaki simply disappeared in less than a second. Chance was kinder to the people in Kokura; they survived. But there is even more to the story.

MASTERING THE CONCEPT

4-1: Central tendency refers to three slightly different ways to describe what is happening in the center of a distribution of data: the mean, the median, and the mode.

Five years after the bombing, an American statistician named W. Edwards Deming persuaded Japan’s leading engineers and businesspeople that a simple statistical insight could lead the devastated nation to economic recovery: Low variability means high reliability. Consumers want things that work and are willing to pay more for reliable products. For Japan, controlling variability translated into developing thousands of small manufacturing solutions that transformed Japanese products from cheap junk into merchandise of exceptional quality. Consider that this took place in a small country where the landscape, people, and morale had just been ravaged by war.

Variability is the central idea driving this powerful insight, and in this chapter, we learn about three ways to measure the variability of any observations we make: range, variance, and standard deviation. But to fully understand variability, we first have to know what observations are varying from—that is, the central tendency, or the middle of a distribution.