# Statistics Concepts Every Data Scientist Should Know

Data scientists are in high demand and in some cases, data scientists are taking over legacy statistician roles. While a career in data science might sound interesting and available, prospective data scientists should consider their comfort with statistics before planning their next step, like earning a master’s degree in data science.

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While a career in data science might sound interesting and available, prospective data scientists should consider their comfort with statistics before planning their next step, like earning a master’s degree in data science.

## Role of Statistics in Data Science

Statistics, as an academic and professional discipline, is the collection, analysis and interpretation of data. Professionals who work with statistics also have to be able to communicate their findings. As such, statistics is a fundamental tool of data scientists, who are expected to gather and analyze large amounts of structured and unstructured data and report on their findings.

Data is raw information, and data scientists learn how to mine it, according to Data Science Central. Data scientists use a combination of statistical formulas and computer algorithms to notice patterns and trends within data. Then, they use their knowledge of social sciences and a particular industry or sector to interpret the meaning of those patterns and how they apply to real-world situations. The purpose is to generate value for a business or organization.

To become a data scientist, you must have a strong understanding of mathematics, statistical reasoning, computer science and information science. You must understand statistical concepts, how to use key statistical formulas, and how to interpret and communicate statistical results.

## Important Statistics Concepts in Data Science

According to Elite Data Science, a data science educational platform, data scientists need to understand the fundamental concepts of descriptive statistics and probability theory, which include the key concepts of probability distribution, statistical significance, hypothesis testing and regression. Bayesian thinking is also important for machine learning; its key concepts include conditional probability, priors and posteriors, and maximum likelihood.

### Descriptive Statistics

Descriptive statistics is a way of analyzing and identifying the basic features of a data set. Descriptive statistics provide summaries and descriptions of the data, as well as a way to visualize the data. A lot of raw information is difficult to review, summarize and communicate. With descriptive statistics, you can present the data in a meaningful way.

Important analyses in descriptive statistics include normal distribution (bell curve), central tendency (the mean, median, and mode), variability (25%, 50%, 75% quartiles), variance, standard deviation, modality, skewness and kurtosis, according to Towards Data Science, a data science industry blog.

Descriptive statistics are separate from inferential statistics. Descriptive statistics show what the data is; inferential statistics are used to reach conclusions and draw inferences from the data.

### Probability Theory

Probability theory is a branch of mathematics that measures the likelihood of a random event occurring, according to Encyclopedia Britannica. A random experiment is a physical situation with an outcome that can’t be predicted until it’s observed. Like flipping a coin. Probability is a quantifiable number between zero and one that measures the likelihood of a certain event happening. The higher the probability (the closer to one), the more likely it is to happen. The probability of flipping a coin is 0.5 since landing on heads or tails is equally likely.

Probability looks at what might happen based on a large amount of data — when an experiment is repeated over and over. It doesn’t make any conclusions regarding what might happen to a specific person or in a specific situation. Statistical formulas related to probability are used in many ways, including actuarial charts for insurance companies, the likelihood of the occurrence of a genetic disease, political polling and clinical trials, according to Britannica.

## Statistical Features

Statistical features are often the first techniques data scientists use to explore data. Statistical features (PDF, 21.6 MB) include organizing the data and finding the minimum and maximum values, finding the median value, and identifying the quartiles. The quartiles show how much of the data falls under 25%, 50% and 75%. Other statistical features include the mean, mode, bias and other basic facts about the data.

## Probability Distributions

A probability distribution is all possible outcomes of a random variable and their corresponding probability values between zero and one, according to Investopedia. Data scientists use probability distributions to calculate the likelihood of obtaining certain values or events.

The probability distribution has a shape and several properties that can be measured, including the expected value, variance, skewness and kurtosis. The expected value is the average (mean) value of a random variable. The variance is the spread of the values of a random variable away from the average (mean). The square root of the variance is known as the standard deviation, which is the most common way of measuring the spread of data.

## Dimensionality Reduction

Dimensionality reduction is the process of reducing the dimensions of your data set, (PDF, 751 KB) according to University of California Merced. The purpose of this is to resolve problems that arise with data sets in high dimensions that don’t exist in lower dimensions. In other words, there are too many factors involved. The more features included in a data set, then the more samples scientists need to have every combination of features represented. This increases the complexity of the experiment. Dimensionality reduction has a number of potential benefits, including less data to store, faster computing, fewer redundancies and more accurate models.

## Over- and Under-Sampling

Not all data sets are inherently balanced. Data scientists use over-sampling and undersampling to alter unequal data sets, (PDF, 4.9 MB) which is also known as resampling. Over-sampling is used when the currently available data isn’t enough. There are established techniques for how to imitate a naturally occurring sample, like Synthetic Minority Over-Sampling Technique (SMOTE). Under-sampling is used when a part of the data is over-represented. Under-sampling techniques focus on finding overlapping and redundant data to use only some of the data.

## Bayesian Statistics

The International Society for Bayesian Analysis explains the Bayes Theorem: “In the Bayesian paradigm, current knowledge about the model parameters is expressed by placing a probability distribution on the parameters, called the prior distribution.”

The prior distribution is a scientist’s current knowledge of a subject. When new information comes to light, it is expressed as the likelihood, which is “proportional to the distribution of the observed data given the model parameters.” This new information is “combined with the prior to produce an updated probability distribution called the posterior distribution.”

This might be confusing for new statistics students, but there are simplified definitions. Bayesian thinking encompasses updating beliefs based on new data, according to Elite Data Science. This is an alternative to frequency statistics, which is commonly used to calculate probabilities.

## Use Statistics and Data Science

If you are eager to learn more about statistics and how to mine large data sets for useful information, data science might be right for you. Competency in statistics, computer programming and information technology could lead you to a successful career in a wide range of industries. Data scientists are needed almost everywhere, from health care and science to business and banking. Learn and compare online master’s in data science programs to decide if it’s a good fit for you.