Introduction to Descriptive Statistics

Once you have collected data, what will 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. You may have no clue about the house prices, so you might ask your real estate agent to give you a sample data set of prices. Looking at all the prices in the sample often is overwhelming. A better way might be to look at the median price and the variation of prices. The median and variation are just two ways that you will learn to describe data. Your agent might also provide you with a graph of the data.

In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called “Descriptive Statistics.” You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

A statistical graph is a tool that helps you learn about the shape or distribution 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 data clusters and where there are only a few data values. Newspapers and the Internet 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. Then, more formal tools may be applied. If we are able to determine the distribution itself it opens up ways for us to analyze the population. We will look at that approach at the end of the chapter when we examine the Normal Distribution.

Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.

Learning Objectives

Below are the learning objectives for each section of this chapter.

4.1 Presenting Categorical Data Graphically

• Create a frequency table
• Create bar graphs
• Create Pie Charts
• Identify common graphical mistakes

4.2 Presenting Quantitative Data Graphically

• Create and interpret Histograms
• Create and interpret frequency polygons
• Create and interpret basic stem and leaf displays
• Identify common graphical mistakes with graphical representation of quantitative data

4.3 Measures of Central Tendency

• Calculate the Mean, Median, and Mode for quantitative data

4.4 Measures of Variation

• Calculate the range.
• Calculate the standard deviation and variance for both a population and sample.
• Calculate the five-number summary.
• Create a box-plot.
• Applications of Box Plots.

4.5 Normal Distribution

• Describe features of a normal distributions
• Use the Empirical Rule (68-95-99.7 Rule) with applications involving the normal distribution
• Find z-scores for values based on a normal distribution
• Find a percentile for a given z-score using the standard normal table
• Solve applied problems involving normal distributions and the standard normal table

Attributions

This page contains modified content from David Lippman, “Math In Society, 2nd Edition.” Licensed under CC BY-SA 4.0.

This page contains modified content from “OpenStax Introductory Satistics” by Barbara Illowsky, Susan Dean. Licensed under CC BY 4.0.