Statistics is a field of mathematical analysis combining linear algebra, calculus involving differential equations, probability theory, and other related disciplines to better understand data. It operates off the premise the collection of data in a limited sense can be useful in summarizing and forecasting information about a much wider population.

The etymological definition of statistics comes from the Latin statisticus, meaning the study and description of politics. It came into the English language more recently from the German word “statistik,” meaning the description of a state or country. Of course, statistics have a far wider range of applications than political polling or evaluating data about country and statewide demographics.

The field of statistics is one subset of the broader discipline known as applied mathematics, and it does indeed have plenty of applications. It enables computer science professionals, businesspeople, social science experts, and government officials to draw conclusions about a whole population from smaller representative sample data.

Since it’s almost always impossible to take in data about an entire population, accurate statistics can provide you with as incisive a degree of insight as possible.

There are multiple ways to depict a dispersion of statistical data. Bar graphs, histograms, pie charts, and scatterplots are just some of the methods to illustrate your visual data analysis. Combining this sort of parametric (and nonparametric) representation with statistical tests like chi-square analysis can help you better grasp the nature of the data before you.

There are two primary types of statistics: descriptive and inferential.

Descriptive statistics focus on depicting data as it stands. There’s not much emphasis on experimental design, as you’re not testing for changes so much as providing a basic criterion for how things are already. You can then use your descriptive statistical data as a variable set upon which to experiment.

Inferential statistics, on the other hand, revolve around testing the reliability of descriptive statistics and experimenting with data. This might mean performing certain tests (like analysis of variance (ANOVA) or regression analysis) to better grasp the statistical significance of the data before you.

Statistical models require certain inputs. Here are seven key elements you’ll need to know about to put this mathematical theory into practice:

1. Central tendency: In a normal distribution, you can expect a wide bell curve at the center of your diagram. This is because there’s likely to be a sample mean (a collection of similar data points around an average) that will serve as your central tendency. Median and mode are two other primary measures of central tendency.

2. Hypotheses: In any form of statistical inference, you’ll need to engage in hypothesis testing. You’ll use a null hypothesis (a description of how things stand currently) and an alternative hypothesis (a description of how you think things might change under experimental conditions). You then use mathematical techniques to test both hypotheses. Make sure to avoid both Type I and Type II standard errors (wrongly affirming or rejecting a null hypothesis respectively).

3. Qualitative data: Some sets of data focus on certain qualities rather than anything numerical. Suppose someone wants to buy ten thousand brown horses. Qualitative data collection would focus on the horses themselves as well as their color rather than the quantity the person wants to buy.

4. Quantitative data: Quantitative data points represent numerical facts. Imagine someone plans to survey fifty people of all different demographics. The demographics themselves would be an example of qualitative data, whereas the numerical data there are fifty different survey participants would be quantitative.

5. Sample size: To form a probability distribution, you need to set your population parameters by collecting a relevant sample size. You’ll then test for additional information (like confidence intervals) based on this data. This statistical data can include both qualitative and quantitative variables.

6. Variability: As frequency distributions stretch out from their centers, there’s a certain amount of variability. This includes things like kurtosis, skewness, and standard deviation. These account for the outliers in your statistical data.

7. Variables: In a broader sense, your random sample of qualitative and quantitative variables makes up two broader independent and dependent variable sets. These enable you to experiment with data by comparing how things are to how they change when you experiment with them.

Developing a working understanding of probability and statistics sets you up to use this branch of applied mathematics in many different pragmatic scenarios. Here are three real-world examples in which mathematical statistics are useful:

• Financial analysis: Wall Street traders and other investors use statistical methods for stock forecasting. These provide the greatest possible insight into how certain securities might perform in the future. The bigger the sample space and size for your financial data, the more thorough your analysis will be.
• Medical trials: Doctors and researchers use interactive statistical trials to test new drugs. By utilizing various theorems and sets of data, they can determine whether these medicines will have a positive effect on a population by analyzing how a sample set of people respond.
• Political polling: Statistical theory helps political prognosticators better predict and poll how people feel about issues and candidates. Data sets like these have a profound and categorical effect on rival parties jockeying for power.