The Basics of Statistics for Data Science By Statisticians

statistics for data science

Data science has become a boom in the current industry. It is one of the most popular technologies these days. Most of the statistics students want to learn data science. 

Because statistics is the building block of the machine learning algorithms. But most of the students don’t know how much statistics they need to know to start data science. 

To overcome this problem, we will share with you the best ever tips on statistics for data science. In this blog, you are going to see which statistics are crucial to start with data science. 

But before moving to the details, let’s check the list of education that you need to become a data scientist.

This graph shows that statistics is one of the major subjects that a data scientist must learn. Now, let’s move to the details of statistics.

Introduction to Statistics

Statistics is one of the most crucial subjects for students. It has various methods that are helpful to solve the most complex problems of real life. 

Statistics is almost everywhere. Data science and data analysts use it to have a look at the meaningful trends in the world. Besides, statistics has the power to drive meaningful insight from the data.

Statistics offers a variety of functions, principles, and algorithms. That is helpful to analyze raw data, build a Statistical Model and infer or predict the result.

An infographic illustrates what you should know about statistics for data science.

What are the basic Terminologies in Statistics?

Before getting started with data science, we have to be well aware of the key statistical terminologies.

  • The population: It is the set of the given sources from which the data has to be collected. There can be a huge population.
  • Sample: It is the subset of data that is extracted from the given Population.
  • Variable: It is the characteristics, number, or quantity of the data that can be measured or counted. In other words, the variable is the data item.
  • Statistical model: The statistical model is also known as statistical Parameter or population parameter. 

What are the different types of Analysis?

Statistics has two types of analysis.

  • Quantitative Analysis: Quantitative Analysis is also known as statistical analysis. It is the science or the art of collecting and interpreting data with numbers and graphs. We also use it to identify patterns and trends.
  • Qualitative Analysis: Qualitative is also known as Non-Statistical Analysis. It gives generic information. It also uses text, sound, and other forms of media.
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Key point: Data TypesNumerical: Numerical data types are those data types that are expressed with digits. These data types are measurable. There are two major types of data types, i.e., discrete and continuous.Categorical: Categorical data types are qualitative data, and it is classified into categories. There are two types of major categorical data types, i.e., nominal (no order) or ordinal (ordered data).

What are the measures in statistics?

Measures of Central Tendency

  • Mean:  Means stands for the average of the given dataset.
  • Median: Median is the middle of the given ordered dataset.
  • Mode: Mode is the most common value in a given dataset. It is only relevant for discrete data.

Measures of Variability

  • Range: Range is the difference between the maximum and minimum values in a given dataset.
  • Variance (σ2): Variance measures how to spread out a set of the given data is relative to the mean.
  • Standard Deviation (σ): It is also a measurement of how spread out numbers are in the given data set.  The Square root of the variance is also known as standard deviation.
  • Z-score: Z score determines the number of standard deviations a data point is from the mean.
  • R-Squared: R square is a statistical measure of fit. It is used to indicate how much variation of a dependent variable is explained by the independent variable(s). We can use it only for simple linear regression.
  • Adjusted R-squared: It is similar to the R squared and also R square modified version. It has been adjusted for the number of predictors in the model. It decreases if the old term improves the model more than would be expected by chance and vice versa.

What are the measurements of Relationships between Variables?

  • Covariance: If we want to find the difference between two variables, then we use the covariance. It is based on the philosophy that if it is positive, they tend to move in the same direction. 

Or if it’s negative, then they tend to move in opposite directions. There will also be no relation with each other if they are zero.

  • Correlation: Correlation is all about measuring the strength of a relationship between two different variables. It ranges from -1 to 1. It is the normalized version of covariance. 

Most of the time, the correlation of +/- 0.7 represents a strong relationship between two different variables. On the other hand, there is  no relationship between variables when the correlations between -0.3 and 0.3

Probability Distribution Functions

  • Probability Density Function (PDF): It is for continuous data. At this moment in the continuous data, the value at any point can be interpreted as providing a relative likelihood. In addition, the value of the random variable will also be equal to that sample.
  • Probability Mass Function (PMF): In the probability mass function for discrete data. It also gives the probability of a given occurring value.
  • Cumulative Density Function (CDF): The cumulative density function is used to tell us the probability that the random variable is less than a certain value. In addition, it is also the integral of the PDF.
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Continuous Data Distributions

  • Continuous Distribution: Continuous data distribution is a probability distribution. In this distribution, all the outcomes are equally likely.
  • Normal/Gaussian Distribution: The normal distribution is commonly referred to as the bell curve. In addition, it is also related to the central limit theorem. It has a standard deviation of 1, and the mean is 0.
  • T-Distribution: The T distribution is another probability distribution. It is used to estimate population parameters when the sample size is small. 
  • Uniform Distribution: In this probability distribution, we have a single value that only occurs within a certain range. The value outside this range is just 0. It is also known as on and off distribution. 
  • Position Distribution: It is quite similar to the normal distribution. But it offers the additional factor, i.e., the skewness. The lower the value of the skewness, the distribution will relatively uniformly spread in all directions. 

But if the skewness is high, then the data will spread out in different directions with unequal distribution.

Discrete Data Distributions

  • Poisson Distribution: One of the most common probability distributions. It expresses the probability of a given number of events occurring within a given fixed time period.
  • Binomial Distribution: It is the probability distribution of the number of successes in a sequence of n independent experiences. And its own Boolean-valued outcome will be as p, 1-p.
  • Moments
  • The Moments describe different aspects of nature and the shape of any given distribution. Moments happened in sequence; therefore, the means is the first moment, the variance is the second one, skewness is the third one, and kurtosis is the fourth one and the last one.


Probability is all about the likelihood that the event is occurring.

  • Conditional Probability:- In this probability, [P(A|B)] is the likelihood of an event occurring. The event occurring is based on the occurrence of an event that occurred previously.
  • Bayes’ Theorem: The Bayes’ theorem is the most popular mathematical formula. It is used to determine conditional probability. 

It is based on the methodology that the probability of A given B is equal to the probability of B given A times the probability of A over the probability of B”.


  • True positive: It detects the condition if the condition is present. 
  • True negative: It does not detect the condition if the condition is not present.
  • False-positive: It automatically detects the condition if the condition is absent.
  • False-negative: It does not detect the condition if the condition is present.
  • Sensitivity: It measures the ability of a test to detect the condition. If the condition is present. The sensitivity = TP/(TP+FN)
  • Specificity: It measures the ability of a test to correctly exclude the condition if the condition is absent. It specificity = TN/(TN+FP)
  • Predictive value positive: Predictive value positive is also called precision. In this, the proportion of positives correspond to the presence of the condition. Here is the formula  PVP = TP/(TP+FP)
  • Predictive value negative: In this, the proportion of negatives and also corresponds to the absence of the condition. Here is the formula PVN = TN/(TN+FN)
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List of statistical skills that are helpful for data scientists!

There are some primary skills that data statistics must have. And these are:

The data scientist must know the method of defining the statistics answers to make effective decisions.
It is necessary that data scientists should know how to apply mathematical statistics, like the central limit theorem or more.
Calculating the statistical measures and data visualization techniques are used to communicate findings. That is why it is necessary for data scientists to understand.
Understanding the relationship between independent and target variables is useful in data science.
ANOVA is one of the best tools used by data scientists to solve statistics problems.
It is always beneficial to know the methods to calculate metrics, such as alpha, p-value, type 1, type2, and so on.

What are the best resources to learn statistics for data science?

Once you get familiar with the statistics concepts that you have to learn for data science, it’s time to know the best resources. There are several resources that are available online as well as offline. 

The best online resources can be:


On the other hand, the best offline or in-hand study material can be books for you. The top 5 books to learn statistics for data science are:

  • Think Stats – by Allen B. Downey

Best fitted for: Beginners with basic Python.

List of topics covered:

Distributions.Statistical thinking.Correlation.Hypothesis testing.
  • Bayesian Methods for Hackers by Cameron Davidson-Pilon

Best fitted for: Non-statisticians who have practical knowledge of Python.

List of topics covered:

Loss functions.Bayesian inference.Priors.Bayesian machine learning.
  • Statistics in Plain English by Timothy C. Urdan

Best fitted for: Non-statisticians who have programming experience.

List of topics covered:

Distributions.Regression.Probability.Factor analysis.
  • Computer Age Statistical Inference by Bradley Efron and Trevor Hastie

Best suited for: Someone who has a basic knowledge of statistics and statistical notation. 

List of topics covered:

Large scale hypothesis testing.Bayesian and frequentist inference.Deep learning.Machine learning.
  • Practical Statistics for Data Scientists by Peter Bruce and Andrew Bruce

Best fitted for: Complete beginners.

List of topics covered:

Descriptive statistics.Data structures.Machine learning.Probability.

Bonus Point:

What are the best practical learning tips?

It has been seen that several universities have designed their courses to check the students’ knowledge. Universities check whether the students can define terminologies, solve equations, and identify plots instead of focusing on the things that apply to solve real-life problems.

Because of this reason, students look for the best practical learning tips. Below are the two techniques that help you to learn statistics for data science.

Top-down approach
Suppose you are assigned to design a model for testing the two versions of products’ efficiency. The product is assumed to enhance the user experience and engagement over the online portal.
With the help of a top-down approach, it is necessary that first, you must understand the problem in-depth. When the motive of the problem is clear, you can easily apply the statistical methods.
This helps you to stay engaged and provide you the best practical learning approach.
Bottom-up approach
This approach is applied by most of the online courses and universities to teach statistics for data science. 
The main purpose of this technique is to teach the theoretical concepts with their history, mathematical notations, and methods to implement them.
For most learners like me, this approach is not useful as it loses interest in learning the theoretical concepts. Moreover, it might not be suitable to learn the problem-solving concepts of statistics.
Therefore, I recommend you go with the top-down approach to learn statistics for data science. But if you want to learn the theoretical concepts also, then go for the bottom-down approach.


Now we have gone through all the basic concepts of statistics for data science. If you are going to start with data science, you should try to command all these statistical concepts.

It will help you a lot when you start learning data science. With the help of these concepts, you will be able to understand the data science concepts. So what are you waiting for? Grab the best statistics books and start learning these concepts.If you are already learning python and need help with python homework, we will provide you the best python homework help. We are also offering python programming homework help and help with python homework.

Frequently Asked Questions

How do I learn statistics for data science?

Above, I have mentioned all the useful terms (like mean, median, and many more) that you should know. Moreover, you can learn the concepts from the above-mentioned books, such as Practical statistics for data science and much more.

Do data scientists use calculus?

Almost all data scientists use calculus for each model. And Gradient Descent IS one of the basic but outstanding examples of calculus in ML (Machine Learning).

Is Data Science in demand?

As per a report, it has been seen that a 29% jump in demand for data scientists. Demand for data science specialists is increasing as companies support themselves with data-driven insights.