David Semmelroth

Summary statistical measures represent the key properties of a sample or population as a single numerical value. This has the advantage of providing important information in a very compact form. It also simplifies comparing multiple samples or populations. Summary statistical measures can be divided into three types: measures of central tendency, measures of central dispersion, and measures of association.

Probability distributions is one of many statistical techniques that can be used to analyze data to find useful patterns. You use a probability distribution to compute the probabilities associated with the elements of a dataset: Binomial distribution: You would use the binomial distribution to analyze variables that can assume only one of two values.

A histogram is a graph that represents the probability distribution of a dataset. A histogram has a series of vertical bars where each bar represents a single value or a range of values for a variable. The heights of the bars indicate the frequencies or probabilities for the different values or ranges of values.

Hypothesis testing is a statistical technique that is used in a variety of situations. Though the technical details differ from situation to situation, all hypothesis tests use the same core set of terms and concepts. The following descriptions of common terms and concepts refer to a hypothesis test in which the means of two populations are being compared.

You identify the center of a dataset with several different summary measures. These include the big three: mean, median, and mode. You calculate the mean of a dataset by adding up the values of all the elements and dividing by the total number of elements. For example, suppose a small dataset consists of the number of days required to receive a package by the residents of an apartment complex: 1, 2, 2, 4, 7, 9, 10 The mean of this dataset would be the following: The average length of time for the residents to receive a package is 5 days.

The two basic types of probability distributions are known as discrete and continuous. Discrete distributions describe the properties of a random variable for which every individual outcome is assigned a positive probability. A random variable is actually a function; it assigns numerical values to the outcomes of a random process.

Several different types of graphs may be useful for analyzing data. These include stem-and-leaf plots, scatter plots, box plots, histograms, quantile-quantile (QQ) plots, and autocorrelation plots. A stem-and-leaf plot consists of a “stem” that reflects the categories in a data set and a “leaf” that shows each individual value in the data set.

One important way to draw conclusions about the properties of a population is with hypothesis testing. You can use hypothesis tests to compare a population measure to a specified value, compare measures for two populations, determine whether a population follows a specified probability distribution, and so forth.

Measures of association quantify the strength and the direction of the relationship between two data sets. Here are the two most commonly used measures of association: Covariance Correlation Both measures are used to show how closely two data sets are related to each other. The main difference between them is the units in which they are measured.