50 Statistic and Probability Interview Questions for Data Scientists

Data scientist probability interview questions and answers for practice in 2021 to help you nail your next data science interview.

50 Statistic and Probability Interview Questions for Data Scientists
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As a data science aspirant, you would have probably come across the following phrase more than once:

“A data scientist is a person who is better at statistics than any programmer and better at programming than any statistician.”

Before data science became a well-known career path, companies would hire statisticians to process their data and develop insights based on trends observed. Over time, however, as the amount of data increased, statisticians alone were not enough to do the job. Data pipelines had to be created to munge large amounts of data that couldn’t be processed by hand.

The term ‘data science’ suddenly took off and became popular, and data scientists were individuals who possessed knowledge of both statistics and programming. Today, many libraries are available in languages like Python and R that help cut out a lot of the manual work. Running a regression algorithm on thousands of data points only takes a couple of seconds to do.

However, it is still essential for data scientists to understand statistics and probability concepts to examine datasets. Data scientists should be able to create and test hypotheses, understand the intuition behind statistical algorithms they use, and have knowledge of different probability distributions.


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As a data scientist, if you are presented with a large dataset, you need to have the ability to understand the type of data pre-processing and analysis to do. You should understand the data presented along with the business requirement and decide the kind of model you should build to make predictions on the dataset. To become a data scientist, here are some statistical concepts you need to understand:

  • Descriptive statistics

  • Measures of central tendency

  • Covariance

  • Correlation

  • Central Limit Theorem

  • Types of Probability distribution

  • Hypothesis Testing

  • Type I and Type II Errors

  • Statistical Models — Linear Regression, Logistic Regression

  • Dimensionality Reduction 

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There are many statistics textbooks and online courses that cover the above topics. You should take some time to learn the theory behind these concepts before making the transition into data science.

What probability and statistics questions are asked in a data science interview ?

This is of the most common questions we get asked at ProjectPro from data science aspirants preparing for a data scientist job interview. This article will cover some of the most commonly asked statistic and probability interview questions and answers to help you prepare for your next data science interview.

If you read up on the above mentioned topics on probability and statistics for data science and answer these questions with confidence, you will be able to ace the probability and statistics part of your data science interview pretty easily.

50 Statistic and Probability Interview Questions and Answers for Data Scientists

Probability Interview Questions for Data Science

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1. What is the difference between quantitative and qualitative data?

Quantitative data is data defined by a numeric value such as a count or range—for example, a person’s height in cm. Qualitative data is described as a quality or characteristic and is usually presented in words. For example, using words like ‘tall’ or ‘short’ to describe a person’s height.

2. Name three different types of encoding techniques when dealing with qualitative data.

Label Encoding, One-Hot Encoding, Binary Encoding

3. Explain the bias-variance trade-off.

The bias-variance trade-off is the trade-off between the error introduced by the bias and the error introduced by a model’s variance. A highly biased model is too simple and doesn’t fit well enough to the training data. 

A model with high variance fits exceptionally well to the training data and cannot generalize outside the data it was trained on. The bias-variance trade-off involves finding a sweet spot to build a machine learning model that fits well enough onto the training data and can generalize and perform well on test data.

4. Give examples of machine learning models with high bias

Linear Regression, Logistic Regression

5. Give examples of machine learning models with low bias

Decision Trees, Random Forest, SVM

6. What is sensitivity and specificity in machine learning with an example?

If we build a machine learning model to predict the presence of a disease in a person, then sensitivity is the true positive rate. The proportion of people who have the disease that received a positive prediction is called sensitivity.

The proportion of people who don’t have the disease who received a negative prediction is called specificity.

7. What is the difference between a Type I and Type II error?

A type I error occurs when the null hypothesis is true but is rejected. A type II error occurs when the null hypothesis is false but isn’t rejected.

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8. What are the assumptions made when building a linear regression model?

  • There is a linear relationship between the dependent variable (Y) and the independent variable (X).

  • Homoscedasticity

  • The independent variables aren’t highly correlated with each other (multicollinearity)

  • The residuals follow a normal distribution and are independent of each other.

9. Name three different types of validation techniques.

  • Train-test split

  • LOOCV (Leave One Out Cross Validation)

  • K-Means Cross-Validation

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10. What is multicollinearity? How does it impact the performance of a regression model?

Multicollinearity occurs when two or more independent variables in the dataset are highly correlated with each other. In a regression model, multicollinearity can harm the interpretability of the model because it will be difficult to distinguish the individual effects of each variable on the model.

11. What is regularization? Why is it done?

Regularization is applied to introduce some noise into models to prevent overfitting. This is usually done by penalizing models with larger weights. A model with larger weights increases in complexity, so regularization aims to choose the simplest possible model and maintain a trade-off between the model’s bias and variance.

12. What does the value of R-squared signify?

The value of R-squared tells us the amount of change in the dependent variable (Y) that is explained by the independent variable (X). The R-squared value can range from 0 to 1. 

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13. What is the Central Limit Theorem?

The Central Limit Theorem states that as the sample size gets larger, the distribution of the sample mean gets closer to the actual population distribution. This means that as the sample size increases, the sample error will reduce.

14. What is the five-number summary in statistics? 

The five-number summary includes the minimum, first quartile, median (second quartile), third quartile, and maximum. It gives us a rough idea of what our variable looks like and can be visualized easily with the help of a box plot.

15. Explain the process of bootstrapping.

If there are limited samples of the actual population, bootstrapping is used to sample repeatedly from the sample population. The sample mean will vary for each resample, and a sampling distribution will be created based on these sample means.

16. List three ways to mitigate overfitting.

  • L1 and L2 regularization 

  • Collect more samples

  • Using K-fold cross-validation instead of a regular train-test split

17. How do you deal with missing data?

There are several ways you can handle missing data based on the number of missing values and type of variable:

  • Deleting missing values

  • Imputing missing values with the mean/median/mode

  • Building a machine learning model to predict the missing value based on other values in the dataset

  • Replacing missing values with a constant

18. What are confounding variables?

A confounding variable is a factor that affects both the dependent and independent variables, making it seem like there is a causal relationship between them.

For example, there is a high correlation between ice cream purchases and forest fires. The number of forest fires and ice cream sales increases at the same time. This is because the confounding variable between them is heat. As temperature rises, so does ice cream sales and the risk of forest fires.

19. What is A/B testing? Explain with an example.

A/B testing is a mechanism used to test user experience with the help of a randomized experiment. For example, a company wants to test two versions of their landing page with different backgrounds to understand which version drives conversions. A controlled experiment is created, and two variations of the landing page are shown to different sets of people.

20. Explain three different types of sampling techniques.

  • Simple random sampling: The individual is selected from the true population entirely by chance, and every individual has an equal opportunity to get selected.

  • Stratified sampling: The population is first divided into multiple strata that share similar characteristics, and each strata is sampled in equal sizes. This is done to ensure equal representation of all sub-groups.

  • Systematic sampling: Individuals are selected from the sampling frame at regular intervals. For example, every 10th member is selected from the sampling frame. This is one of the easiest sampling techniques but can introduce bias into the sample population if there is an underlying pattern in the true population.

21. If a model performs very well on the training set but poorly on the test set, then the model is  __________.

Answer: Overfitting

22. Explain the terms confidence interval and confidence level.

A confidence interval is a probability that the true population parameter falls between a range of two estimates. The level of confidence (for example, 95% or 99%) refers to the certainty that the true parameter lies within the confidence interval as multiple samples are repeatedly taken.

23. What is a p-value?

A p-value is a probability of obtaining the observed result if the null hypothesis were true. We can set a threshold for the p-value based on the hypothesis created, and if the p-value falls below this threshold, then there is little to no chance that the observed result could have occurred. This gives us enough evidence to reject the null hypothesis.

24. What is standardization? Under which circumstances should data be standardized?

Standardization is the process of putting different variables on the same scale. Variables are made to follow a standard normal distribution with a mean of 0 and a standard deviation of 1.

Standardizing data can give us a better idea of extreme outliers, as it is easy to identify values that are 2–3 standard deviations away from the mean. Standardization is also used as a pre-processing technique before feeding data into machine learning models so that all variables are given the same weightage.

25. What are some properties of a normal distribution? Give some examples of data points that follow a normal distribution.

  • The mean, median, and mode in a normal distribution are very close to each other.

  • There is a 50% probability that a value will fall on the left of the normal distribution, and a 50% probability that a value will fall on the right.

  • The total area under the curve is 1.

Example: Values like a population’s height and IQ are normally distributed.

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26. When is it a good idea to use the mean as a measure of central tendency?

When data follows a normal distribution, it is good to use the mean as a measure of central tendency. However, if data is skewed to the left or right, this skewness will pull the mean along with it, so it is better to use the median as a measure of central tendency.

27. Explain the difference between ridge and lasso regression.

Ridge regression or L2 regression, adds the sum of the square of weights as a penalty to the model’s cost function. Lasso regression or L1 regression, adds absolute weights to the model’s cost function.

Lasso regression can also be used as a feature selection technique, as it can pull feature weights down to zero and eliminate variables that aren’t necessary.

28. What is the law of large numbers? Provide an example.

According to the law of large numbers, as an experiment is repeated independently multiple times, the result of the investigation becomes closer to the expected value.

For example, if we toss a coin 1000 times, the probability of seeing heads in the coin tosses will be closer to 0.5 than if we tossed the coin 100 times.

29. How can outliers be identified?

Outliers can be identified by finding the first and third quartile. Any value lesser than Q1 — 1.5 X IQR or Q3 + 1.5 X 1QR is considered an outlier.

30. When is it better to use an F1 score over accuracy to evaluate a model?

The F1 score is the harmonic mean of a model’s precision and recall. In the case of imbalanced datasets, the F1 score provides us a better measure of model performance than accuracy.

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31. What is selection bias?

When obtaining a sample population, selection bias is a bias introduced when randomization isn’t completely achieved. This means that the sample population won’t represent the true population, as a subset of the true population is left out.

32. What are some ways to overcome an imbalanced dataset?

An imbalanced dataset is a dataset that has an over-representation of certain classes and an under-representation of others. Machine learning models often make incorrect predictions when this happens, as they tend to make a majority class prediction.Oversampling or undersampling can be done to overcome an imbalanced dataset. Oversampling is randomly selecting data from the minority class and adding them to the training dataset, increasing the representation of minority class samples.

Undersampling is the opposite — the majority of class samples are selected and removed at random to create a more balanced distribution of all classes in the dataset.

33. When should you use a t-test and a z-test?

A z-test is used when the population variance is known or if the population variance is unknown but the sample size is large.

A t-test is used when the population variance is unknown, and the sample size is small.

34. What is the difference between a homoscedastic and heteroscedastic model?

When the variance of dependent variables is consistent for all data points, then a model is homoscedastic. All data points will be of a similar distance from the regression line. 

Heteroscedasticity is the opposite, and a model is said to be heteroscedastic if the variance is different for all data points.

35. Which model generally performs better in making predictions — random forests or decision trees? Explain why.

Random forests typically perform better than decision trees. This is because it overcomes most of the limitations of decision trees. Large decision trees usually lead to overfitting. Random forests overcome this issue by selecting only a subset of variables at each split, ensuring that the model built can generalize better.

The output of multiple weak learners is combined to come up with a single prediction, which tends to be more accurate than the output of a single large decision tree. 

36. How can overfitting be detected when building a prediction model?

Overfitting can be detected by using K-Fold cross-validation for training and testing.

37. Is it possible for a poor classification model to have high accuracy? If so, why does this happen?

Poor classification models like a model that simply predicts the majority class can perform well in terms of accuracy. For example, if 90% of the samples in the dataset tested negative for disease and 10% tested positive — a model that predicts negative on all data points will have a 90% accuracy, which is exceptionally high.

However, model performance is still poor, and accuracy isn’t indicative of how good the model is in this case.

38. There is a right-skewed distribution with a median of 70. What can we conclude about the mean of this variable?

The mean of this variable will be over 70, as the positive skew will pull the mean along with it.

39. What is a correlation coefficient? 

A correlation coefficient is an indicator of how strong the relationship between two variables is. A coefficient near +1 indicates a strong positive correlation, a coefficient of 0 indicates no correlation, and a coefficient near -1 indicates a strong negative correlation.

40. What does it mean if an independent variable has high cardinality? How does this impact model performance?

Cardinality refers to the number of categories a single categorical variable has. If a variable has high cardinality, it means that it has many different types associated with it.

This can negatively impact model performance if not correctly encoded.

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41. What are the different types of selection bias? Explain them.

  • Sampling bias: This is the bias introduced by non-random sampling. For example, if you were to survey all university students to understand their view on gender disparity but only surveyed female students. This would introduce a bias into the model and wouldn’t provide a complete picture of the true population.

  • Confirmation bias: This is a bias caused by the tendency of an individual to favor information that validates their own beliefs.

  • Time-interval bias: This is bias caused by selecting observations that only cover a specific range of time. This can skew the samples collected because it limits the data collected to a specific set of circumstances.

42. What are the assumptions made when building a logistic regression model?

  • Absence of outliers that can strongly impact the model

  • Absence of multicollinearity

  • There should be no relationship between the residuals and the variable.

43. Explain the bagging technique in random forest models.

Bagging stands for bootstrap aggregation. In random forests, the dataset is sampled multiple times using the bootstrap technique with replacement. Weak learners are trained independently on each sample with different features to split on at each node. Finally, the average or majority class prediction is provided as output to the user.

44. Describe three error metrics for a linear regression model.

The three most commonly used error metrics to evaluate the performance include the MSE, RMSE, and MAE.

  • MSE: The mean squared error measures the average squared difference between true and predicted values across all data points. 

  • RMSE: The RMSE (root mean squared error) takes the square root of the mean squared error.

  • MAE: The mean absolute error takes the average absolute difference between the true and predicted values across all data points.

45. Explain the impact of seasonality on a time-series model.

When building a time-series model, seasonality is a factor that can impact the model’s performance. These are cycles that repeat over a certain time and need to be accounted for in the model that is being built. Otherwise, there is a risk of making inaccurate predictions.

For example, let’s say you want to build a model that predicts the number of hoodies sold in the next few months. If you only use data from the beginning of the year to make the prediction and don’t take into account the previous year, you won’t account for seasonal variations in buying patterns. People would buy lesser hoodies in March and April as they did in February because the weather is getting warmer, which isn’t accounted for by the machine learning model.

46. What is the default threshold value in logistic regression models? 

The default threshold value in logistic regression models is 0.5.

47. Is it possible to change this threshold? Describe a situation that might require you to control the threshold value.

Yes, it is possible to change the threshold of a logistic regression model. For example, in situations where we want to identify more true positives and build a model with high sensitivity, we can reduce the threshold value so that a slightly lower than 0.5 can also be considered a positive prediction.

48. Differentiate between univariate and bivariate analysis.

The univariate analysis only summarizes one variable at a time. Measures of variance and central tendency are examples of univariate analysis. Bivariate analysis analyzes the relationship between two variables — such as correlation or covariance.

49. Given two variables Y1 and Y2, provide some code in Python or R to calculate the correlation between these variables.

# Python:

np.corrcoef(Y1, Y2) 

# R:

cor(Y1,Y2)

50. If there is sufficient evidence to reject the null hypothesis at a 5% significance level, then there is sufficient evidence to reject it at a 1% significance level.” Is this statement true or false, and explain why.

This statement is sometimes true. Since we don’t know the actual p-value, we can’t tell if the null hypothesis will be rejected. If the p-value was smaller than 0.01, there is sufficient evidence to reject the null hypothesis at a 1% significance level. However, if the p-value was around 0.04, it wouldn’t be possible to reject the null hypothesis at a 1% significance level.

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Ace Your Next Data Science Interview

The probability and statistic interview questions and answers provided above are by no means an exhaustive list. Depending on the type and seniority of the data science job role you are applying for, the set of questions at a data science interview can differ.

However, the questions above cover a broad range of statistical for data science. If you are able to answer the questions listed above then you have a strong grasp of the underlying statistics behind the machine learning models, along with an understanding of different data types. This indicates that you are prepared to ace the statistics aspect of data science interviews.

It is also worth mentioning that data science is a fairly broad field, and there are many different hats you can put on as a data scientist. Depending on the company you’re working at, and the kind of expertise they require, the level of statistical knowledge required for a job can differ.

Some data science roles are more geared towards data engineering and model deployment, while others are more quantitative and require you to analyze and build models. Depending on the role you apply for, you will get a different set of challenges presented to you during the interview.

If you are looking to get a data science job that involves quantitative analysis and model building, then it is essential to answer the questions presented above. Make sure to do a lot of practice on real-world hands-on data science projects that explore hypothesis testing, sampling, probability distributions, and the Central Limit Theorem. Also, make sure to understand the statistics behind standard linear and tree-based models.



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