Caltech Bootcamp / Blog / /

The Ultimate Guide to Statistics Interview Questions for Data Scientists

Statistics Interview Questions for Data Scientists

Cracking a statistics interview for a data scientist role takes a lot of work. It is a vast area with plenty of complexities. If you’re an aspiring data scientist looking to land your dream job, you’d want to know which statistics interview questions to prepare for and how to answer them.

This guide will walk you through the most commonly asked data science statistics interview questions and their answers. You’ll also learn how to prepare for statistics interviews and understand the importance of data science programs in your preparation.

Why Do Data Scientists Need to Know About Statistics?

The beauty of statistics lies in its ability to create meaningful insights from seemingly chaotic data sets. So, there are plenty of reasons why a data scientist should be well-versed in statistics.

Fundamental Component of Data Science

This is the most obvious one. Statistics is one of the most important disciplines for data scientists. Data science techniques and methodologies are built on statistics.

Data Analysis and Interpretation

Data scientists use statistics to gather, review, analyze, and draw meaningful conclusions from data. It helps them make sense of complex datasets and extract valuable insights.

Machine Learning and Algorithms

Machine learning algorithms are based on statistics. Data scientists use statistical methods to capture and translate data patterns into actionable evidence. This is how predictive models are built to enable data-driven decisions.

Minimizing Risk and Uncertainty

Decision-making requires a quantitative and objective framework. Statistics provides this, which helps minimize risk and uncertainty by basing decisions on data and evidence. There is no room for intuition or gut feelings.

Interdisciplinary Nature of Data Science

Data science is a multifaceted field. It combines computer science, statistics, mathematics, and domain expertise. It allows data scientists to bridge the gap between data and real-world applications.

Career Opportunities

Proficiency in statistics opens up many career opportunities in data science, from data analysis to machine learning research.

In summary, statistics is essential to data science because it underpins data analysis, machine learning, and decision-making. Aspiring data scientists should consider adding this key skill to their repertoire.

Also Read: Why Use Python for Data Science?

Top Statistics Interview Questions for Beginners

When you enter the world of data science, you are most likely to be met with questions that show how well you know the basics. These questions are some of the most common ones that you can expect.

#1. What is the Central Limit Theorem?

The Central Limit Theorem is a fundamental concept in statistics. It states that when you take a sufficiently large sample from a population and calculate the mean of that sample, the distribution of those sample means will approximate a normal distribution. This holds true even if the original population does not follow a normal distribution. The Central Limit Theorem is fundamental for many statistical calculations. It is used in confidence intervals and hypothesis testing.

#2. Describe Hypothesis Testing. How is the statistical significance of an insight assessed?

Hypothesis Testing is a statistical method used to determine if a particular experiment or observation yields meaningful results. It involves defining a null hypothesis and an alternative hypothesis. An insight’s statistical significance is assessed by calculating a p-value. If the p-value is less than a predetermined significance level (alpha), the null hypothesis is rejected, showing that the results are statistically significant.

#3. What is the Pareto principle?

The Pareto principle, also known as the 80/20 rule, suggests that 80 percent of the effects or results in a given situation are typically generated by 20 percent of the causes. For example, 80 percent of sales come from 20 percent of customers in business.

#4. What is the Law of Large Numbers in statistics?

The Law of Large Numbers in statistics states that as the number of trials or observations in an experiment increases, the average or expected value of the results will approach the true or expected value. This principle demonstrates the convergence of sample statistics to population parameters with a larger sample size.

#5. What are observational and experimental data in statistics?

Observational data is gathered through observational studies. One can come to conclusions by observing certain variables without manipulation. Experimental data, on the other hand, is collected through controlled experiments where variables are intentionally manipulated to study cause-and-effect relationships.

#6. What is an outlier?

An outlier is a data point within a data set that significantly deviates from the rest of the observations. Outliers can affect the accuracy and efficiency of statistical models and analyses and should often be removed from the data set.

#7. How do you screen for outliers in a data set?

Outliers can be screened using various methods. Two common approaches include:

  • Standard deviation/z-score: Calculate the z-score for each data point and identify those with z-scores significantly above or below a certain threshold.
  • Interquartile range (IQR): Calculate the IQR, which represents the range of values within the middle 50% of the dataset, and identify data points outside this range.

#8. What is the meaning of an inlier?

An inlier is a data point within a dataset that is consistent with the majority of other observations. Unlike outliers, inliers do not significantly deviate from the central tendency of the data.

#9. What is the assumption of normality?

It refers to the assumption that the distribution of sample means, particularly across independent samples, follows a normal (bell-shaped) distribution. This assumption is essential for many statistical tests and models.

#10. What is the meaning of Six Sigma in statistics?

In statistics, Six Sigma refers to a quality control methodology aimed at producing a data set or process that is nearly error-free. It is typically measured in terms of standard deviations (sigma), and a process is considered at the six sigma level when it is 99.99966% error-free, indicating high reliability.

#11. What is the meaning of KPI in statistics?

KPI stands for key performance indicators in statistics. It is a quantifiable metric to assess whether specific goals or objectives are being achieved. KPIs are crucial for measuring performance in various contexts, such as organizations, projects, or individuals.

#13. What are some of the properties of a normal distribution?

The normal distribution is also known as the Gaussian distribution. It has key properties, including symmetry, unimodality (a single peak), and the mean, median, and mode, all equal and located at the center. It forms a bell-shaped curve when graphed.

#14. How would you describe a ‘p-value’?

A p-value is a statistical measure calculated during hypothesis testing. It represents the probability of observing data as extreme as what was obtained in the experiment if the null hypothesis were true. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting that the results are statistically significant.

#15. How can you calculate the p-value using MS Excel?

In MS Excel, you can calculate the p-value using the TDIST function. The formula is =tdist(x,deg_freedom, tails). The p-value is expressed in decimals and can be calculated using Excel’s Data Analysis tool by selecting the relevant column and specifying the confidence level and other variables.

#16. What are the types of biases that you can encounter while sampling?

Sampling biases can occur in research and surveys, and there are various types, including:

  • Undercoverage bias
  • Observer Bias
  • Survivorship bias
  • Self-Selection/Voluntary Response Bias
  • Recall Bias
  • Exclusion Bias

Also Read:A Beginner’s Guide to the Data Science Process

Data Science Statistics Interview Questions for Experienced Candidates

If you already have some years of experience within the data science world, you will be moving to advanced areas. You can expect questions focusing on specific areas of expertise and even generally tougher ones. This is to check your proficiency in advanced levels.

#1. Explain the concept of a statistical interaction.

A statistical interaction occurs when the influence of one input variable on an output variable depends on the value of another input variable. For example, in tea stirring, adding sugar alone may not impact sweetness, and stirring alone may not either. However, when you combine both (sugar and stirring), the interaction results in increased sweetness. Statistical interactions are crucial in understanding complex relationships in data analysis and modeling.

#2. Give an example of a dataset with a non-Gaussian distribution.

Bacterial growth is an example of a dataset with a non-Gaussian or exponential distribution. In such datasets, the values are typically skewed to one side of the graph, unlike the symmetrical bell curve of a Gaussian (normal) distribution. Non-Gaussian distributions are common in various real-world processes and phenomena.

#3. What are the key assumptions necessary for linear regression?

Linear regression relies on several key assumptions:

  • Linearity: The relationship between predictor variables and the outcome variable is linear.
  • Normality: The errors (residuals) are normally distributed.
  • Independence: Residuals are independent of each other, meaning one observation’s error does not affect another’s.
  • Homoscedasticity: The variance of residuals is constant across all levels of predictor variables. Violations of these assumptions can affect the model’s accuracy and reliability.

#4. When should you opt for a t-test instead of a z-test in statistical hypothesis testing?

You should choose a t-test for a small sample size (n<30). It can also be used when the population standard deviation is unknown. A z-test is appropriate for more extensive samples (n>30). It is used when the population standard deviation is known. The t-test uses the t-distribution, which accounts for the more significant uncertainty in smaller samples.

#5. Describe the difference between low and high-bias Machine Learning algorithms.

Low-bias machine learning algorithms, such as decision trees and k-nearest Neighbors, have the flexibility to capture complex patterns in data. Preconceived notions less constrain them and can fit the data closely.

In contrast, high-bias algorithms like Linear Regression and Logistic Regression have simpler models and make stronger assumptions. They may not fit the data as closely but are less prone to overfitting small variations in the data.

#6. What is cherry-picking, P-hacking, and the practice of significance chasing in statistics?

Cherry-picking is the selective presentation of data that supports a specific claim while ignoring contradictory data.

P-hacking involves manipulating data analysis to find statistically significant patterns even when no real effect exists.

Significance chasing, also known as Data Dredging or Data Snooping, involves presenting insignificant results as if they are almost significant, potentially leading to misleading conclusions.

#7. Can you outline the criteria that must be met for Binomial distributions?

Three main criteria must be met for a Binomial distribution:

  • A fixed number of observation trials are conducted.
  • Each trial is independent, meaning the outcome of one trial doesn’t affect others.
  • The probability of success remains constant across all trials. These criteria ensure the Binomial distribution’s applicability in scenarios where events are binary and follow a specific probability of success.

#8. What is the Binomial Distribution Formula used for?

The Binomial Distribution Formula, b(x; n, P), is used to calculate the probability of getting a specific number of successes (x) in a fixed number of independent trials (n). Here, each trial has a constant probability of success (P). It’s commonly used in scenarios like coin tosses. It helps you know the probability of getting certain heads or tails in a given number of flips.

#9. Define linear regression and its application in statistical modeling.

Linear regression is a statistical technique used to model the relationship between one or more predictor variables and a single outcome variable. It is commonly used to quantify the linear association between variables in predictive modeling. Linear regression helps understand how changes in predictor variables impact the outcome, making it a valuable tool in various fields, including economics, healthcare, and social sciences.

#10. Explain the distinction between type I and type II errors in hypothesis testing.

Type I error occurs when the null hypothesis is incorrectly rejected, suggesting an effect exists when it doesn’t (false positive). Type II error occurs when the null hypothesis is incorrectly accepted, failing to detect a real effect (false negative). These errors affect the accuracy of statistical tests and decision-making in hypothesis testing.

Also Read:What Is Data Mining? A Beginner’s Guide

More Statistics Interview Questions for Experienced Candidates

#1. Explain the concept of degrees of freedom (DF) in statistics.

Degrees of freedom (DF) in statistics represent the number of options or variables available to analyze a problem. It’s a critical concept used primarily with the t-distribution and less commonly with the z-distribution.

An increase in degrees of freedom allows the t-distribution to approximate the normal distribution more closely. When DF exceeds 30, the t-distribution closely resembles a normal distribution. In essence, degrees of freedom determine the flexibility of statistical analysis and the shape of the distribution.

#2. What are some of the characteristics of a normal distribution?

A normal distribution, often called a bell-shaped curve, possesses several key properties:

  • Unimodal: It has only one mode or peak.
  • Symmetrical: The left and right halves mirror each other.
  • Central tendency: The mean, median, and mode are all centered at the midpoint of the distribution.

These properties make the normal distribution a fundamental statistical model, as many natural phenomena approximate this distribution.

#3. Given a 30 percent chance of seeing a supercar in a 20-minute interval, what’s the probability of seeing at least one in an hour (60 minutes)?

To find the probability of seeing at least one supercar in 60 minutes when there’s a 30 percent chance in a 20-minute interval, we calculate the probability of not seeing any supercar in 20 minutes and then raise it to the third power (as there are three 20-minute intervals in 60 minutes). The probability of not seeing any supercar in 20 minutes is 0.7 (1 – 0.3), so the probability of not seeing any supercar in 60 minutes is (0.7)^3 = 0.343. Therefore, the probability of seeing at least one supercar in 60 minutes is 1 – 0.343 = 0.657.

#4. Define sensitivity in the context of statistics.

Sensitivity, often used in the context of classification models such as logistic regression or random forests, measures the accuracy of a model in identifying true positive events. It is calculated as the ratio of correctly predicted true events to the total number of actual true events. Sensitivity helps assess a model’s ability to identify positive cases correctly, which is crucial in various fields like healthcare for disease diagnosis.

#5. What’s the advantage of using box plots?

Box plots concisely represent the 5-number summary (minimum, 1st quartile, median, 3rd quartile, maximum). It also facilitates easy comparison between data groups or distributions, enhancing data analysis and visualization.

#6. What does TF/IDF vectorization represent in natural language processing?

TF/IDF (Term Frequency-Inverse Document Frequency) vectorization is a numerical measure used to assess the importance of words in a document within a larger corpus. It calculates the relevance of a term based on its frequency in the document (TF). At the same time, it also accounts for its rarity across the entire corpus (IDF).

TF/IDF is commonly employed in natural language processing and text mining to identify significant terms in documents for tasks like document classification and information retrieval.

#7. List some examples of low and high-bias machine learning algorithms.

Low-bias machine learning algorithms have greater flexibility to capture complex patterns and include decision trees, k-nearest Neighbors, and support vector machines. High-bias algorithms, like Linear Regression and Logistic Regression, make stronger assumptions and have simpler models, making them less prone to overfitting but potentially missing nuanced relationships in data.

#8. When would the middle value be better than the average value?

When some values are too high or too low and can change the data a lot, the middle value is better because it can show the data more accurately.

#9. How can you use root cause analysis in real life?

Root cause analysis is a way of finding the main cause of a problem by asking why it happened. Examples: You might see that more crimes happen in a city when more red shirts are sold. But this does not mean that one causes the other. You can always use different ways to check if something causes something else.

#10. What is the ‘Design of Experiments’ in statistics?

The Design of Experiments in statistics is a way of planning an experiment that tells you how one thing changes when another changes. It is also called the Design of Experiments.

Also Read: A Data Scientist Job Description: The Roles and Responsibilities in 2024

Tips to Ace Your Data Science Interviews

Preparing for a data science interview can help you anticipate the statistics interview questions you will be asked. More than simply book knowledge, make sure you do these too.

  • Thoroughly research the position and company you are applying to. Know everything you need to know about their culture, values, and methods. When you know this, you can structure your answers accordingly.
  • Before you attend the interview, make sure you are thoroughly aware of the job description. Know what skills are required and what are the duties laid out. Sharpen your skills and resume according to the needs of the job. Data science training can help you with this.
  • Practice well ahead of time. Make sure you have enough time to relax before the interview. Sharpen your soft skills and make yourself presentable. These little things go a long way for formal meetings.

Take the Next Steps and Arm Yourself With the Skills for a Bright Career

Building a career in data science and statistics can be daunting. But when you practice enough with these interview questions and explore independently, you are raising your chances. In addition to a solid academic background, get involved in programs like our data science bootcamp to gain well-rounded skills.

In this program, you will learn the core concepts of data science, strengthen your basics, and build skills in highly relevant areas like generative AI and prompt engineering.

With 25+ hands-on projects and a diverse curriculum covering mathematics, programming, SQL, data visualization, machine learning, and more, this bootcamp prepares you for leading data science careers.

You might also like to read:

Data Collection Methods: A Comprehensive View

What Is Data Processing? Definition, Examples, Trends

Differences Between Data Scientist and Data Analyst: Complete Explanation

What Is Data Collection? A Guide for Aspiring Data Scientists

What Is Data? A Beginner’s Guide

Data Science Bootcamp

Leave a Comment

Your email address will not be published.

Why Python for Data Science

Why Use Python for Data Science?

This article explains why you should use Python for data science tasks, including how it’s done and the benefits.

Data Science Bootcamp


6 months

Learning Format

Online Bootcamp

Program Benefits