2.1 Introduction to Descriptive Statistics and Frequency Tables (7/16) -- Significant Statistics

2.1 Introduction to Descriptive Statistics and Frequency Tables 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 the spread of quantitative data - Recognize, describe, and calculate the measures of location of quantitative data - Identify outliers in quantitative data 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 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 and calculate, and even more importantly, how to 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 relative standing of a single observation with regards 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 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. The type of graph you choose to use first depends on the type of data you are working with. 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 the time series plot in special cases. The emphasis 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, or how often each value occurs in the set. Frequency tables can be used to show either quantitative or cat