The purpose of descriptive statistics is to present a mass of data in a more understandable form. We may summarize the data in numbers as (a) some form of average, or in some cases a proportion, (b) some measure of variability or spread, and (c) quantities such as quartiles or percentiles, which divide the data so that certain percentages of the data are above or below these marks. Furthermore, we may choose to describe the data by various graphical displays or by the bar graphs called histograms, which show the distribution of data among various intervals of the varying quantity. It is often necessary or desirable to consider the data in groups and determine the frequency for each group. This chapter will be concerned with various summary numbers, and the next chapter will consider grouped frequency and graphical descriptions. Use of a computer can make treatment of massive sets of data much easier, so computer calculations in this area will be considered in detail. However, it is necessary to have the fundamentals of descriptive statistics clearly in mind when using the computer, so the ideas and relations of descriptive statistics will be developed first for pencil-and-paper calculations with a pocket calculator. Then computer methods will be introduced and illustrated with examples. First, consider describing a set of data by summary numbers. These will include measures of a central location, such as the arithmetic mean, markers such as quartiles or percentiles, and measures of variability or spread, such as the standard deviation. 3.1 Central Location Various “averages” are used to indicate a central value of a set of data. Some of these are referred to as means. (a) Arithmetic Mean Of these “averages,” the most common and familiar is the arithmetic mean, defined by 1 N x or µ= ∑xi N i=1
