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.

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.

Measures of central tendency show the center of a data set. Three of the most commonly used measures of central tendency are the mean, median, and mode. Mean Mean is another word for average. Here is the formula for computing the mean of a sample: With this formula, you compute the sample mean by simply adding up all the elements in the sample and then dividing by the number of elements in the sample.

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.

Unlike a stem-and-leaf plot, a scatter plot is intended to show the relationship between two variables. It may be difficult to see whether there's a relationship between two variables just by looking at the raw data, but with a scatter plot, any patterns that exist in the data become much easier to see. A scatter plot consists of a series of points; each point shows a single value for two different variables.

Regression analysis is used to estimate the strength and direction of the relationship between variables that are linearly related to each other. Two variables X and Y are said to be linearly related if the relationship between them can be written in the form Y = mX + b where m is the slope, or the change in Y due to a given change in X b is the intercept, or the value of Y when X = 0 As an example of regression analysis, suppose a corporation wants to determine whether its advertising expenditures are actually increasing profits, and if so, by how much.

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.

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.

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.