Descriptive Statistics

Abstract

Abstract This chapter introduces descriptive statistics, that is, how numbers are used to summarize and describe data gathered in quantitative research. Prior to analysis, it’s important to examine the values in your database (i.e., spreadsheet) and examine it for data entry errors or anomalies. Next, you should always visualize your data via plots and summarize the data by calculating measures of frequency, central tendency, and variability. For interval-/ratio-level data, you can also create histograms and box plots to visualize frequency distributions. The mean, median, and mode are measures of central tendency that will help you understand the most “representative” or “typical” single value. In a normal distribution (i.e., bell curve), the mean, median, and mode are the same. Interval-/ratio-level data are also often described according to the degree to which the values follow the shape of normal distribution properties. Measures of variability provide the degree of spread among values in a distribution. These include minimum/maximum values, range, variance, standard deviation, and quartiles. When data do not conform to a normal distribution, indices other than the mean and standard deviation, such as the median, mode, minimum, maximum, range, and quartiles, should be used to describe the central tendency and variability of that variable. Frequency counts and percentages are often used to summarize ordinal- and nominal-level data, and bar plots are used to visualize such data.