Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 8

Measures of Center

Who tends to speak more quickly in a presidential debate: Republicans or Democrats? How much does an average male Olympic rower weigh? Does it matter whether or not we consider the coxswain to be a rower? If you are considering buying a house, is it meaningful to ask for the “average” price of houses sold in the area? How often do houses cost less than the average value? Averages such as these are commonly reported in news articles and product advertisements, but these averages can be misleading and misunderstood. For example, would comparing averages be a meaningful way to investigate whether or not cancer pamphlets are written at an appropriate level to be read and understood by cancer patients? You will investigate properties of averages and other measures of center in this topic.

Overview

In the previous topic, you examined distributions of quantitative data, representing them graphically with stemplots and histograms and describing their key features such as center, spread, shape, clusters, and outliers. When analyzing distributions of quantitative data, it is also handy to use a single numerical measure to summarize a certain aspect of a distribution, such as its center. In this topic, you will encounter some common measures of the center of a distribution, investigating their properties, and applying these measures to some real data, while exposing some of their limitations.

Preliminaries

1. Who do you expect to speak more quickly in a presidential ...