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.

You can use the Central Limit Theorem to convert a sampling distribution to a standard normal random variable. Based on the Central Limit Theorem, if you draw samples from a population that is greater than or equal to 30, then the sample mean is a normally distributed random variable. To determine probabilities for the sample meanthe standard normal tables requires you to convertto a standard normal random variable.

After you estimate the population regression line, you can check whether the regression equation makes sense by using the coefficient of determination, also known as R2 (R squared). This is used as a measure of how well the regression equation actually describes the relationship between the dependent variable (Y) and the independent variable (X).

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 statistic is said to be robust if it isn’t strongly influenced by the presence of outliers. For example, the mean is not robust because it can be strongly affected by the presence of outliers. On the other hand, the median is robust — it isn’t affected by outliers. For example, suppose the following data represents a sample of household incomes in a small town (measured in thousands of dollars per year): 32, 47, 20, 25, 56 You compute the sample mean as the sum of the five observations divided by five: The sample mean is $36,000 per year.

When comparing data samples from different populations, two of the most popular measures of association are covariance and correlation. Covariance and correlation show that variables can have a positive relationship, a negative relationship, or no relationship at all. A sample is a randomly chosen selection of elements from an underlying population.

When a data set contains a large number of repeated values, you can simplify the process of computing the mean by using weights — the frequencies of a value in a sample or a population. You can then compute the geometric mean as a weighted average. You can calculate the weighted geometric mean in the same way for both samples and populations.

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.

An unconditional, or marginal, probability is one where the events (possible outcomes) are independent of each other. When you create a joint probability table, the unconditional probability of an event appears as a row total or a column total. For example, say that you create a joint probability table representing the distribution of students in a business school; you classify them according to major and whether they're working on a bachelor's degree or a master's degree.