2.1 Descriptive Statistics and Frequency Distributions
2.1 Descriptive Statistics and Frequency Distributions
Learning Objectives
By the end of this chapter, the student should be able to:
- Display and interpret categorical data
- Display and interpret quantitative data
- Recognize, describe, and calculate the measures of the center of quantitative data
- Recognize, describe, and calculate the measures of spread of quantitative data
- Recognize, describe, and calculate the measures of location of quantitative data
- Identify outliers in quantitative data
Descriptive Statistics
Once you collect data, what do you do with it? Data can be described and presented in many different formats. For example, suppose you are interested in buying a house in a particular area. If you have no clue about house prices, you might ask your real estate agent to give you a sample dataset of prices, but looking through all the prices can be overwhelming. A better way might be to look at numerical descriptions such as the average or median house price. Your agent might also provide you with a graph of the data.
This area of statistics is called descriptive statistics. We will look at both graphical and numerical descriptive methods. You will learn how to construct, calculate, and, most importantly, interpret these measurements and graphs.
Numerical descriptors consist of summary statistics (typically calculated from a sample) that represent important aspects such as the central tendency and variability of a distribution or the relative standing of a single observation with regard to the rest of the distribution.
Graphical descriptive methods consist of chart, tables, and graphs. These are tools that help you learn about the distribution, or shape, of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where the data clusters and where there are only a few data values. Newspapers and the internet sources use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data before more formal tools are applied.
The type of graph you choose first depends on the type of data with which you are working. Some of the types of graphs used to display categorical data are pie charts and bar charts. Some graphs that are used to summarize and organize quantitative data are the dot plot, the histogram, the stem-and-leaf plot, the frequency polygon, the box plot, and, in special cases, the time series plot. The emphasis here will be on histograms and box plots.
We will start by looking at a graphical method that can display any type of data, the frequency table.
Frequency Tables
Frequency tables are a great starting place for summarizing and organizing your data. Once you have a set of data, you may first want to organize it to see the frequency (how often each value occurs in the set).
Frequency tables can be used to show either quantitative or categorical data. Displaying categorica