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.

Statistical software packages are extremely powerful these days, but they cannot overcome poor quality data. Following is a checklist of things you need to do before you go off building statistical models. Check data formats Your analysis always starts with a raw data file. Raw data files come in many different shapes and sizes.

Before you apply statistical techniques to a dataset, it's important to examine the data to understand its basic properties. You can use a series of techniques that are collectively known as Exploratory Data Analysis (EDA) to analyze a dataset. EDA helps ensure that you choose the correct statistical techniques to analyze and forecast the data.

When testing a hypothesis for a small sample where you have to find the appropriate critical right-tail value, this value depends on certain criteria. In addition to being positive, the value also depends on the sample size and whether or not the population standard deviation is known. After you calculate a test statistic, you compare it to one or two critical values, depending on the alternative hypothesis, to determine whether you should reject the null hypothesis.

Regression analysis is a statistical tool used for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another — the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate.

Random variables and probability distributions are two of the most important concepts in statistics. A random variable assigns unique numerical values to the outcomes of a random experiment; this is a process that generates uncertain outcomes. A probability distribution assigns probabilities to each possible value of a random variable.