Alan Anderson

Statistics make it possible to analyze real-world business problems with actual data so that you can determine if a marketing strategy is really working, how much a company should charge for its products, or any of a million other practical questions. The science of statistics uses regression analysis, hypothesis testing, sampling distributions, and more to ensure accurate data analysis.

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.

Quartiles split up a data set into four equal parts, each consisting of 25 percent of the sorted values in the data set. Quartiles are related to percentiles like so: First quartile (Q1) = 25th percentile Second quartile (Q2) = 50th percentile Third quartile (Q3) = 75th percentile Because the second quartile is the 50th percentile, it's also the median of a data set.

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.

In statistics, sampling distributions are the probability distributions of any given statistic based on a random sample, and are important because they provide a major simplification on the route to statistical inference. More specifically, they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values.

Regression analysis is one of the most important statistical techniques for business applications. It's a statistical methodology that helps estimate the strength and direction of the relationship between two or more variables. The analyst may use regression analysis to determine the actual relationship between these variables by looking at a corporation's sales and profits over the past several years.

As with the binomial and geometric distributions, you can use simple formulas to compute the moments — expected value, variance, and standard deviation — of the Poisson distribution. How to calculate the expected value of the Poisson distribution You can find the expected value of the Poisson distribution by using the formula, For example, say that on average three new companies are listed in the New York Stock Exchange (NYSE) each year.

When testing a hypothesis for a small sample where you have to find the appropriate critical left-tail value, this value depends on certain criteria. In addition to being negative, the value also depends on the sample size and whether or not the population standard deviation is known. A left-tailed test is a test to determine if the actual value of the population mean is less than the hypothesized value.

A probability distribution is a formula or a table used to assign probabilities to each possible value of a random variable X. A probability distribution may be either discrete or continuous. A discrete distribution means that X can assume one of a countable (usually finite) number of values, while a continuous distribution means that X can assume one of an infinite (uncountable) number of different values.