Top 50 Statistics Interview Questions and Answers

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Statistics are crucial in modern computing and data management. Hence, many companies spend billions on it. This field is exciting, and many organizations use analytics. We’ve, therefore, compiled standard statistics interview questions and answers to prepare for interviews. Also, we’ve answered standard statistics questions to help with your job interview. Thus, the topics covered include hypothesis testing, the central limit theorem, Six Sigma, KPI, error, p-values, bias, and more.

What is Statistics?

The most crucial element of data science is statistics. Additionally, it involves collecting, processing, investigating, decoding, and communicating data. Furthermore, every field of research uses statistics to collect, analyze, interpret, and present numerical data. Moreover, data science depends on statistics to make sense of the data. In addition, statistics is used in scientific, industrial, and social fields to understand populations or data models.

There are primarily two classes of Statistics:

Descriptive statistics 

Firstly, a type of statistics where we outline the data through the given compliances is called Descriptive statistics. Additionally, summarizing is done from samples using mean or standard deviation variables. Moreover, descriptive statistics can classify, depict, and explain a group of data using tables, graphs, and figure norms. For example, a cluster of individuals in a city using distinct services such as the internet or television channels.

The descriptive statistics can be classified below:

• Measure of frequency.
• Estimate of position.
• Measure of dispersion.
• A measure of central tendency.

Inferential statistics

Inferential statistics is a kind of statistics employed to solve the purpose of descriptive statistics. These statistics help us finish the data relying on arbitrary deviations such as observational mistakes, sampling deviations, etc. Once we have gathered, investigated, and outlined the data, we use them to define the purpose of the assembled data. It also enables us to give information beyond the known data or information.

Basic Statistics Interview Questions

Here are a few basic statistics interview questions.

1. How is the statistical importance of an insight evaluated?

Hypothesis testing is employed to discover the statistical significance of the insight. To elaborate, first, we state the null and alternate hypotheses and then compute the p-value.

After computing the p-value, the null hypothesis is considered authentic, and the values are specified. Also, the alpha value, which represents the significance, is tweaked to fine-tune the result. We abandon the null hypothesis if the p-value is smaller than the alpha. It guarantees that the consequence acquired is statistically noteworthy.

2. Where are long-tailed distributions used?

A long-tailed allocation is one in which the tail gradually fades as the curve approaches its end. In addition, the product sales allocation and the Pareto principle are good examples of long-tailed distributions. Also, we use it widely to classify and for regression problems.

3. What is the central limit theorem?

The central limit theorem states that the normal distribution arrives when the sample size varies without affecting the population distribution’s shape. This central limit theorem is the key because we use it widely to perform hypothesis testing and accurately calculate confidence intervals.

4. What are the distinctions between experimental and observational data in Statistics?

Observational data is associated with the data received from observational investigations. Additionally, we monitor variables to see if there is any correlation between them.  Moreover, We derive experimental data from experimental studies where particular variables are stable to see if any dissimilarity exists in the work.

5. What is the mean imputation for missing data? Why is it deemed a bad practice?

Mean imputation is a seldom-used technique where void values in a dataset are substituted directly with the related mean of the data. Contrarily, we consider it a bad practice as it clears the accountability for feature correlation. It also means the data will have inferior variance and improved bias, adding to the dip in the model’s accuracy alongside fewer confidence intervals.

6. What is an outlier? How are outliers specified in a dataset?

Outliers are data points that vary broadly compared to other observations in the dataset. Depending on the learning process, an outlier can deteriorate a model’s accuracy and sharply decrease efficiency. We determine outliers using the following two methods:

• Standard deviation/z-score.
• Interquartile range (IQR).

7. How do we handle missing data in statistics?

We address the missing data in the following ways:

• Projection of the missing values.
• Designation of individual (unique) values.
• Omission of rows that have missing data.
• Mean or median imputation.
• Using arbitrary forests helps the missing values.

8. What is exploratory data analysis?

Exploratory data analysis is conducting investigations on data to comprehend the data agreeably. Additionally, initial investigations specify patterns, find abnormalities, examine hypotheses, and inspect if the assumptions are correct.

9. What is the definition of selection bias?

Firstly, selection bias is a phenomenon that involves choosing individual or grouped data in a way we do not consider to be random. Randomization plays a crucial role in conducting analysis and comprehending model functionality satisfactorily. Additionally, the resulting sample will only accurately represent the population if we achieve correct randomization.

10. Name the different kinds of selection bias in statistics. 

There are different kinds of selection bias, as shown below:

• Observer selection.
• Attrition.
• Protopathic bias.
• Time intervals.
• Sampling bias.

11. What is the meaning of an inlier?

A data point on the same level as the leftovers of the dataset is called an inlier. Discovering an inlier in the dataset is challenging compared to an outlier, as it demands external data. Inliers, comparable to outliers, diminish model accuracy. Hence, we remove even them if we find them in the data. Thus, we do it to sustain model accuracy at all times.

12. Give an example of root cause analysis.

Root cause analysis, as the name suggests, is a process employed to solve issues by first determining the root cause of the problem. For example, if the crime rate is directly associated with the sales of a red-colored shirt, they have a favorable correlation. However, this does not imply that one compels the other. We can, therefore, test the causation using A/B or hypothesis testing.

13. What is the meaning of Six Sigma in statistics?

Six Sigma is a quality management technique that builds error- or defect-free data sets. Also, we can call a standard deviation Sigma or σ. Additionally, with a higher standard deviation, the process will perform less accurately and generate a defect. If a process result is 99.99966% error-free, it is considered Six Sigma. A Six Sigma model functions better than 1σ, 2σ, 3σ, 4σ, 5σ procedures and is reliable enough to produce defect-free work. 

14 What is the definition of KPI in statistics?

KPI, or key performance indicator, is a quantifiable criterion for comprehending whether a goal is achievable. Additionally, KPI is a dependable metric used to calculate an organization’s or individual’s performance level in relation to their objectives. Moreover, the expense ratio is an example of a KPI in an organization. 

15. Define the Pareto principle.

The Pareto principle, or the 80/20 rule, declares that we can achieve 80% of the consequences or results from 20% of the causes in an investigation. For example, we can reach 80% of customers from 20% of sales.

16. What do we understand about the law of large numbers in statistics?

The law of large numbers defines that an upsurge in the number of trials in an investigation will lead to a positive and proportional boost in the outcomes. Thus, the values are more comparable to the desired value. Let us understand the probability of rolling six-sided cubes three times. The desired value acquired is far from the average value. But, when we roll a dice numerous times, we obtain the average result comparable to the expected value. 

17. List a few properties of a normal distribution.

Normal distribution, or Gaussian distribution, refers to data symmetric to the mean, whereas data far from the mean occurs less frequently. In graphical representation,  a normal distribution is a bell-shaped, symmetrical curve along the axes.

We will list a few properties of a normal distribution:

• Symmetrical – The figure varies with the parameter.
• Unimodal – Has only one mode.
• Mean – the standard of central tendency.
• Central tendency – the median, mean, and mode are at the midpoint, or they are equal, and the curve is symmetrical at the midpoint. 

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

We calculate the P-value in statistics during hypothesis testing, indicating the likelihood of data occurring randomly. Suppose a p-value is 0.5 and is less than alpha. In short, there is a probability of 5% that the experiment results occurred by chance or 5% of the time.

19. What types of biases do you have to face while sampling?

During an investigation or a survey, sampling bias occurs when you need a fair representation of data samples. The six primary classes of biases are as follows:

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

20. What is the definition of standard deviation?

The standard deviation measures data spread. Moreover, a low value means the data is close to the average. Conversely, a high value indicates that data is widely dispersed.

21. What is a bell-curve distribution?

A normal distribution is a bell curve distribution. It gets its name from the bell curve shape we obtain when we visualize the distribution.

22. What is skewness?

The absence of symmetry in a data distribution indicates skewness. Additionally, it indicates significant differences between the mean, the mode, and the median of data. Consequently, we cannot use skewed data to create a normal distribution.

23. What is kurtosis?

Kurtosis represents the extreme values found in one tail of distribution versus the other. Additionally, it is the measurement of outliers found in the distribution. Moreover, a high kurtosis value denotes substantial outliers in data. Therefore, we should add more data to the dataset or remove the outliers in such cases. 

Intermediate Statistics Interview Questions

Some of the intermediate statistics interview questions are as follows.

24. What is cherry-picking, P-hacking, and significance chasing?

We define cherry-picking as selecting information that sustains a particular claim and ignoring other claims that refute the desired conclusion.

P-hacking is a process in which we manipulate data collection or analysis until we find significant patterns with no underlying effect. 

Data Dredging, Data Fishing, or Data Snooping are also known as significance chasing. Also, it refers to reporting insignificant results as if they are almost significant. 

25. What is the dissimilarity between type I and type II errors?

A type 1 error occurs when we abandon the null hypothesis even though it is precise. Thus, it is also called a false positive.

A type 2 error arises when the null hypothesis fails to get denied, even though it is wrong. Thus, we call it a false negative.

26. What is a statistical interaction?

A statistical interaction is a phenomenon that emerges when the influence of an input variable affects the output variable. A real-life example comprises the interaction of adding sugar to the tea. Both variables do not impact sweetness, but their combination affects the sweetness.  

27. What are the criteria for Binomial distributions when we use them?

The three main criteria that Binomial distributions must meet are:

• We must fix the number of observation trials. It means that finding probability involves repeating an event several times.
• Every trial has to be independent. This means that the trials should not impact the probability of other trials.
• The probability of success should remain the same through all the trials. 

28. What is linear regression? 

Linear regression models relationships between descriptive variables and one output. For instance, it links predictor variables like age, gender, genetics, and diet to height. 

29. What are the inferences needed for linear regression?

We need four significant inferences for linear regression:

• We must have a linear relationship between the independent and dependent variables. 
•  Autocorrelation is a process in which errors are distributed without correlation. 
• Multicollinearity is a phenomenon with a lack of correlation between independent variables.
• Homoscedasticity is a phenomenon of assumptions that the variation of the outcome or response variables is similar for all independent variable values.

30. What is the empirical rule?

A normal distribution is an empirical rule where every data part is within three standard deviations of the mean. We can call it the 68–95–99.7 rule. According to the rule, the percentage of values in a normal distribution follows the 68%, 95%, and 99.7% rule. We can also say that 68% of values will come under one standard deviation of the mean, 95% within two standard deviations, and 99.75% within three standard deviations of the mean.

31. How are confidence and hypothesis tests similar? Also, how are they different?

Confidence tests and hypothesis tests are fundamental in statistics. The confidence interval is vital for research accuracy, especially in medical studies. Moreover, it gives a range of values to capture unknown parameters. Furthermore, hypothesis testing checks if the results are not random. The formula uses ‘p’ as a parameter. Additionally, these methods estimate parameters and test hypotheses using data samples. Confidence intervals provide precise estimations, while hypothesis testing assesses conclusion accuracy. Also, they work together to infer population parameters. If 0 is in the confidence interval, the sample and population match. Lastly, a high p-value means rejecting the null hypothesis.

32 What conditions must we satisfy to hold the central limit theorem?

The conditions we must satisfy for the central limit theorem to hold:

• The data must follow the randomization condition, meaning we must sample it randomly.
• The Independence Assumptions indicate that the sample values must be independent.
• Sample sizes must be enormous. They must be equal to or greater than 30 to hold CLT. A large sample size is required to maintain the accuracy of CLT to be true. 

33. What is Random Sampling? Could you give some examples of some random sampling techniques?

Random sampling is when every sample has an equal chance of selection. It’s also called probability sampling.

The four primary types of random sampling processes are:

• Simple Random Sampling technique involves choosing a sample randomly. Furthermore, we need a sampling frame with a list of population members. Excel helps to generate random numbers for each element. 
• The Systematic Random Sampling technique is simple and popular in statistics. It works by selecting every kth element in a sequence. For example, you pick one element, skip ‘n’ and choose the next. 

• The Cluster Random Sampling technique groups the population into clusters and selects them randomly.  
• The Stratified Random Sampling technique divides the population into similar groups. Then, we take a random sample from each group for representation.

34. Discuss the dissimilarity between population and sample in inferential statistics. 

We can direct a population in inferential statistics to the entire group from which we get samples and use it to conclude. Contrarily, a sample is a distinctive group from which we take data, and we use this data to calculate the statistics. The sample size is always smaller than that of the population. 

35. What are quantitative and qualitative data?

Qualitative data describes data attributes and is also called Categorical data. But, quantitative data is a standard of numerical values or counts. We also call it Numerical data.

36. What is Bessel’s correction?

Bessel’s correction is the factor we use to estimate a population’s standard deviation from its sample. Consequently, it causes the standard deviation to be less biased, thereby furnishing accurate results.

Advanced Statistics Interview Questions

A few advanced interview questions are listed below.

37. In what scenarios do we keep outliers in data?

The scenarios to keep outliers in data for analysis are:

• Results are critical.
• Outliers add meaning to the data.
• The data is highly skewed.

38. Briefly explain the procedure to estimate the length of all sharks worldwide.

We employ the following steps to determine the length of sharks:

• Specify the confidence level (usually around 95%).
• Utilize sample sharks to calculate.
• Calculate the mean and standard deviation of the lengths.
• Decide t-statistics values.
• Choose the confidence interval in which the mean length lies.

39. How does the width of the confidence interval change with length?

We use the width of the confidence interval to define the decision-making steps. The width increases with the confidence level. The below information also decides:

• A wide confidence interval is unnecessary information.
• A narrow confidence interval is a high-risk factor.

40. What do we understand by the degrees of freedom (DF) in statistics?

Degrees of freedom, or DF, specify the number of choices when investigating. It is used chiefly with t-distribution and not with the z-distribution. As the DF increases,  the t-distribution reaches closer to the normal distribution.  However, if DF is more than 30, then the t-distribution has all the characteristics of a normal distribution. 

41. Mention some of the properties of a normal distribution.

A normal distribution has a bell-shaped and symmetric curve along the axes. A few of the properties of normal distributions are as follows:

• Unimodal has one mode.
• Symmetrical – It means the left and right halves of the curve mirror each other.
• Central tendency – The mean, median, and mode are in the middle.

42. What is the meaning of sensitivity in statistics?

We use sensitivity to determine the accuracy of a classifier (logistic, random forest, etc.). Sensitivity = Predicted True Events/Total number of Events is the simple formula to calculate sensitivity. 

43. What do you understand by left and right skewed distributions?

A left-skewed distribution has the left tail elongated than the right tail. Here, we have the mean < median < mode.

Similarly, a right-skewed distribution has the right tail longer than the left. But, it is mean > median > mode here.

44. Define TF/IDF vectorization. 

The TF/IDF vectorization shows a word’s importance in a document. The document is also known as the collection or corpus. The TF-IDF value increases with word recurrence in a document. It’s critical in Natural Language Processing (NLP), particularly for text mining and information retrieval.

45. What is the use of Hash tables in statistics?

Hash tables are the data structures that denote the representation of structured key-value pairs. Furthermore, a hash table employs the hashing function to calculate an index containing the details of the key mapped to the associated value.

46. What techniques reduce underfitting and overfitting during model training?

Underfitting occurs when data is high bias and low variance. Contrarily, overfitting has high variance and low bias. To reduce underfitting in data, we perform the following tasks:

• Increase model complexity.
• Increase the number of features.
• Remove noise from the data.
• Increase the number of training epochs.

To reduce overfitting in data, we perform the following steps:

• Increase training data.
• Lasso regularization.
• Use random dropouts.

47. Does a symmetric distribution need to be unimodal?

The symmetric distribution need not be unimodal (have one mode or value that happens frequently). It can be either bi-modal (owning two values with the highest frequencies) or multi-modal (having multiple or more than two values with the highest frequencies).

48. What is the effect of outliers in statistics?

Outliers have a negative effect since they skew the outcome of any statistical query. For example, if we want to compute the mean of a dataset having outliers, the mean will differ from the actual mean. 

49. How can we detect overfitting while creating a statistical model? 

Firstly, overfitting is spotted through cross-validation. Secondly, we split the data into parts and go through the dataset. Each time, one part tests, others train. This method ensures thorough training and testing to detect overfitting.

50. What is the relationship between standard deviation and standard variance?

We calculate standard deviation as the square root of standard variance. It shows data spread from the mean. In contrast, standard variance explains data variability from the dataset mean.

What’s Next?

Enroll in Henry Harvin’s Data Science Course to learn more. It’s an 8-hour Two-way Live Online Interactive session. In addition, Henry Harvin presents a one-year Gold Membership of Analytics  Academy that includes e-learning access. Subsequently, the course covers the basics of statistics, collaborating and organizing different data types, evaluating correlation and covariance, etc.

Moreover, this program, led by industry experts with 10+ years of experience, provides valuable perks. These comprise Alumni status, guaranteed internships, weekly job opportunities, and live projects. In addition, it’s a complete package that guarantees practical skills and continuous guidance for professional growth.

Conclusion

Firstly, the Statistics Interview Questions and Answers cover basic to advanced concepts. Additionally, they help students and professionals grasp the field thoroughly. Moreover, exploring the Top 50 Questions offers valuable insights into statistics. Furthermore, they comprise descriptive and inferential statistics, probability theory, and hypothesis testing. In addition, by studying these questions, individuals enhance their statistical understanding. Moreover, practicing them sharpens problem-solving and critical thinking skills. Additionally, being prepared boosts confidence in statistics interviews. Furthermore, reviewing helps identify strengths and areas needing improvement. Lastly, mastering these questions enhances job prospects in data-related roles.

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Frequently Asked Questions

1. How do I prepare for a statistics interview?

You can read the top commonly asked interview questions to prepare for a statistics interview. These questions will help you improve your skills and ace upcoming interviews.

2. Are statistics asked in data science interviews?

Statistics questions are common in any data science interview. Additionally, they range from basics like explaining the measure of central tendency and their impact with the outlier to defining the p-value.

3. What are statistical analysis questions?

We can answer a statistical question by gathering data and where there will be variability in that data.

4. What are the five basic statistics?

The five basic statistics concepts are:

• Regression is a technique for comparing a dependent and independent variable.
• Calculation of the mean.
• Standard deviation.
• Sample size determination.
• Hypothesis testing.

5. What are the basics of statistics?

The basics of statistics comprise the measurement of central tendency and dispersion. Additionally, the central tendencies include mean, median, and mode. Moreover, dispersions comprise variance and standard deviation. Furthermore, the mean is the average of the observations. The median is the mid value when we arrange the observations in order.

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