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.

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.

One technique you can use to identify the distribution a dataset follows is the QQ-plot (QQ stands for quantile-quantile). You can use the QQ-plot to compare a dataset to a large number of different probability distributions. Often, data is compared to the normal distribution because many statistical tests assume normally distributed data.

Prior to performing any type of statistical analysis, understanding the nature of the data being analyzed is essential. You can use EDA to identify the properties of a dataset to determine the most appropriate statistical methods to apply to the data. You can investigate several types of properties with EDA techniques, including the following: The center of the data The spread among the members of the data The skewness of the data The probability distribution the data follows The correlation among the elements in the dataset Whether or not the parameters of the data are constant over time The presence of outliers in the data Another key question EDA answers is "Does the data conform to our assumptions?

A quantile-quantile plot (also known as a QQ-plot) is another way you can determine whether a dataset matches a specified probability distribution. QQ-plots are often used to determine whether a dataset is normally distributed. Graphically, the QQ-plot is very different from a histogram. As the name suggests, the horizontal and vertical axes of a QQ-plot are used to show quantiles.

A time series is a set of observations of a single variable collected over time. With time series analysis, you can use the statistical properties of a time series to predict the future values of a variable. There are many types of models that may be developed to explain and predict the behavior of a time series.

In data analysis, the relationship between the mean and the median can be used to determine if a distribution is skewed. The histogram shows that most of the returns are close to the mean, which is 0.000632 (0.0632 percent). The median is −0.0001179. Histogram shows most returns close to the mean. Here's how to determine whether the distribution is skewed: In this case, the distribution of returns to ExxonMobil stock is positively skewed.

Data is stored in different ways in different systems. So it's no surprise that when collecting and consolidating data from various sources, it's possible that duplicates pop up. In particular, what makes an individual record unique is different for different systems. An investment account summary is attached to an account number.

For time series data, it's important to know whether the observations continue to have the same mean over time and whether the variance of the data is changing over time. Many statistical tests and forecasting techniques depend on this assumption. The figure shows a time series plot of ExxonMobil's daily returns throughout 2013.