Chapter 6
Interpreting Spatial Models1

This chapter aims to do two things. Part A focuses on how to estimate statistics, particularly the mean and standard deviation, from data that is only presented in summary form (like a frequency table or a histogram). Part B takes this one step further, by helping you connect two different ways of picturing data by relating histograms and boxplots. Both give a picture of how the data is spread out. The difference is that a boxplot takes the data and breaks it into four chunks with the same number of observations in each chunk, but with each chunk of data having a different length. Histograms are the opposite: each chunk has exactly the same length, but probably has different numbers of observations in it.

As a result of this chapter, students will learn

As a result of this chapter, students will be able to

Why summarized data cannot be used to compute an accurate mean or standard deviation

What a percentile is

What a cumulative distribution is

Estimate the mean from a set of summarized data

Estimate the standard deviation from a set of summarized data

Sketch a boxplot of the data underlying a histogram without having the data itself

Sketch a rough idea of a histogram of data based only on a boxplot of the data

 6.1 Estimating Stats from Frequency Data
  6.1.1 Definitions and Formulas
  6.1.2 Worked Examples
  6.1.3 Exploration 6A: Data Summaries and Sensitivity
 6.2 Two Perspectives are Better than One
  6.2.1 Definitions and Formulas
  6.2.2 Worked Examples
  6.2.3 Exploration 6B: Stock Investment Decisions
 6.3 Homework
  Mechanics and Techniques Problems
  Application and Reasoning Problems
 6.4 Memo Problem: Portfolio Analysis