Analyzing one categorical variable : Analyzing categorical data Two-way tables : Analyzing categorical data Distributions in two-way tables : Analyzing categorical data. Displaying and comparing quantitative data. Displaying quantitative data with graphs : Displaying and comparing quantitative data Describing and comparing distributions : Displaying and comparing quantitative data More on data displays : Displaying and comparing quantitative data.
Summarizing quantitative data. Measuring center in quantitative data : Summarizing quantitative data More on mean and median : Summarizing quantitative data Interquartile range IQR : Summarizing quantitative data Variance and standard deviation of a population : Summarizing quantitative data.
Variance and standard deviation of a sample : Summarizing quantitative data More on standard deviation : Summarizing quantitative data Box and whisker plots : Summarizing quantitative data Other measures of spread : Summarizing quantitative data.
Modeling data distributions. Percentiles : Modeling data distributions Z-scores : Modeling data distributions Effects of linear transformations : Modeling data distributions.
Density curves : Modeling data distributions Normal distributions and the empirical rule : Modeling data distributions Normal distribution calculations : Modeling data distributions More on normal distributions : Modeling data distributions. Exploring bivariate numerical data. Introduction to scatterplots : Exploring bivariate numerical data Correlation coefficients : Exploring bivariate numerical data Introduction to trend lines : Exploring bivariate numerical data.
Least-squares regression equations : Exploring bivariate numerical data Assessing the fit in least-squares regression : Exploring bivariate numerical data More on regression : Exploring bivariate numerical data.
Study design. Statistical questions : Study design Sampling and observational studies : Study design Sampling methods : Study design. Types of studies experimental vs. Harvard University computer scientist David J. Even at the undergraduate level, it is not uncommon for math and statistics majors to pursue a complementary area of study by minoring or double majoring in a related discipline. Mathematics, for example, has obvious applications in computer science, physics, and engineering, while statistics is itself an application of mathematics that is integral to all of the social sciences psychology, sociology, economics, political science , and also to business and management.
Because statistics is applied mathematics, both disciplines are often housed within the same academic department. In contrast, a BS in mathematics, or in mathematics with a concentration in statistics, will have fewer general education requirements, but may require a secondary concentration in an area like computer science, engineering, education, or business and economics. Pursuing a PhD in mathematics or statistics is generally reserved for those aiming for an upper level research position in academia, industry, or government, and for those who want to teach in these disciplines at the college level.
These are research-intensive degree programs that can require six or more years to complete. The American Mathematical Society has an online tool for exploring graduate degrees in mathematics and statistics. The American Statistical Association has a page devoted to resources for statistics students.
The convergence of computer technology, mathematical theory, and statistical modeling has created what many have termed the Data Revolution, which encompasses everything from public policy and healthcare, to business and marketing strategy, to professional sports and the entertainment industry. Simply put, there are fewer and fewer areas of human endeavor in which quantitative literacy, applied mathematics, and the use of statistics are not highly valued.
There may be no better example of this than FiveThirtyEight. The list below covers a broad but by no means complete breakdown of some of the more prominent fields that are open to those with training in mathematics and statistics:. Mining, storing, sorting, and analyzing big data sets, and designing and maintaining the IT systems that facilitate these processes requires programming knowledge and training in mathematics and statistics.
There are increasingly openings for data scientists and analytics professionals in all sectors of the economy, from government to private industry, in manufacturing and in marketing. Professional data science and analytics resources include the:. Mathematics and statistics have long been an integral component of IT and computer science, and these are areas that mathematicians and statisticians have traditional found employment in. Career opportunities in this sector have been broadening, particularly as concerns about cybersecurity have intensified.
Professional cybersecurity and IT resources include:. Another area that has traditionally been a magnet for those with backgrounds in mathematics and statistics is engineering, which itself is a broad category that includes professionals working in aerospace, biotech, civil, industrial, materials, mechanical, and structural engineering. Professional engineering organizations include:. Actuarial scientists are the statistical and probability specialists who make the insurance industry possible, and who play crucial roles in financial investing and management.
Based on the sample size and distribution statisticians can calculate the probability that statistics, which measure the central tendency, variability, distribution, and relationships between characteristics within a data sample, provide an accurate picture of the corresponding parameters of the whole population from which the sample is drawn. Inferential statistics are used to make generalizations about large groups, such as estimating average demand for a product by surveying a sample of consumers' buying habits or to attempt to predict future events, such as projecting the future return of a security or asset class based on returns in a sample period.
Regression analysis is a widely used technique of statistical inference used to determine the strength and nature of the relationship i. The output of a regression model is often analyzed for statistical significance , which refers to the claim that a result from findings generated by testing or experimentation is not likely to have occurred randomly or by chance but is likely to be attributable to a specific cause elucidated by the data.
Having statistical significance is important for academic disciplines or practitioners that rely heavily on analyzing data and research. Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable's mean, standard deviation, or frequency. Inferential statistics, in contrast, employs any number of techniques to relate variables in a data set to one another, for example using correlation or regression analysis.
These can then be used to estimate forecasts or infer causality. Statistics are used widely across an array of applications and professions. Any time data are collected and analyzed, statistics are being done. This can range from government agencies to academic research to analyzing investments. Economists collect and look at all sorts of data, ranging from consumer spending to housing starts to inflation to GDP growth.
In finance, analysts and investors collect data about companies, industries, sentiment, and market data on price and volume. Together, the use of inferential statistics in these fields is known as econometrics.
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