Statistics Interview Questions
1. What Is Bayesian?
Bayesians condition on the data actually observed and consider the probability distribution on the hypotheses.
2. What Is Frequentist?
Frequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not.
3. What Is Likelihood?
The probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes.
4. What Is P-value?
In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. If the p-value is less than 0.05 or 0.01, corresponding respectively to a 5% or 1% chance of rejecting the null hypothesis when it is true.
5. Give An Example Of P-value?
Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips
- null hypothesis (H0): fair coin;
- observation O: 14 heads out of 20 flips; and
- p-value of observation O given H0 = Prob(≥ 14 heads or ≥ 14 tails) = 0.115.
The calculated p-value exceeds 0.05, so the observation is consistent with the null hypothesis – that the observed result of 14 heads out of 20 flips can be ascribed to chance alone – as it falls within the range of what would happen 95% of the time were this in fact the case. In our example, we fail to reject the null hypothesis at the 5% level. Although the coin did not fall evenly, the deviation from expected outcome is small enough to be reported as being “not statistically significant at the 5% level”.
6. What Is Sampling?
Sampling is that part of statistical practice concerned with the selection of an unbiased or random subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern.
7. What Are Sampling Methods?
There are four sampling methods:
- Simple Random (purely random),
- Systematic( every kth member of population),
- Cluster (population divided into groups or clusters)
- Stratified (divided by exclusive groups or strata, sample from each group) samplings.
8. What Is Mode?
The mode of a data sample is the element that occurs most often in the collection.x=[1 2 3 3 3 4 4]mode(x) % return 3, happen most.
9. What Is Median?
Median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle onemedian(x) % return 3.
10. What Is Quartile?
- second quartile (50th percentile) .
- third quartile (75th percentile) .
- kth percentile.
- prctile(x, 25) % 25th percentile, return 2.25.
- prctile(x, 50) % 50th percentile, return 3, i.e. median.
11. What Is Skewness?
Skewness is a measure of the asymmetry of the data around the sample mean. If skewness is negative, the data are spread out more to the left of the mean than to the right. If skewness is positive, the data are spread out more to the right.Skewness(x) % return-0.5954
12. What Is Variance?
variance describes how far values lie from the mean.var(x) %return 1.1429
13. What Is Kurtosis?
Kurtosis is a measure of how outlier-prone a distribution is.kurtosis(x) % return2.3594
14. What Is Moment?
Quantitative measure of the shape of a set of points.moment(x, 2); %return second moment
15. What Is Covariance?
Measure of how much two variables change together.y2=[1 3 4 5 6 7 8]cov(x,y2) %return 2*2 matrix, diagonal represents variance.
16. What Is One Sample T-test?
T-test is any statistical hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is supported.[h,p,ci] = ttest(y2,0)% return 1 0.0018 ci =2.6280 7.0863
17. What Is Alternative Hypothesis?
The Alternative hypothesis (denoted by H1 ) is the statement that must be true if the null hypothesis is false.
18. What Is Significance Level?
The probability of rejecting the null hypothesis when it is called the significance level α , and very common choices are α = 0.05 and α = 0.01.
19. Give Example Of Central Limit Theorem?
Given that the population of men has normally distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability thata. if 1 man is randomly selected, his weight is greater than 180 lb.b. if 36 different men are randomly selected, their mean weight is greater that 180 lb.Solution:
a) z = (x – μ)/ σ = (180-173)/30 = 0.23For normal distribution P(Z>0.23) = 0.4090b) σ x̄ = σ/√n = 20/√ 36 = 5
z= (180-173)/5 = 1.40
P(Z>1.4) = 0.0808
20. What Is Binomial Probability Formula?
P(x)= p x q n-x n!/[(n-x)!x!]where n = number of trials.x = number of successes among n trials.p = probability of success in any one trial.q = 1 -p.
21. Do You Know What Is Binary Search?
For binary search, the array should be arranged in ascending or descending order. In each step, the algorithm compares the search key value with the key value of the middle element of the array. If the keys match, then a matching element has been found and its index, or position, is returned. Otherwise, if the search key is less than the middle element’s key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right.
22. Explain Hash Table?
A hash table is a data structure used to implement an associative array, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the correct value can be found.
23. Explain Central Limit Theorem?
As the sample size increases, the sampling distribution of sample means approaches a normal distribution.If all possible random samples of size n are selected from a population with mean μ and standard deviation σ, the mean of the sample means is denoted by μ x̄ , so,μ x̄ = μthe standard deviation of the sample means is:σ x̄ = σ⁄√ n
24. What Is Null Hypothesis?
The null hypothesis (denote by H0 ) is a statement about the value of a population parameter (such as mean), and it must contain the condition of equality and must be written with the symbol =, ≤, or ≤.
25. What Is Linear Regression?
Modeling the relationship between a scalar variable y and one or more variables denoted X. In linear regression, models of the unknown parameters are estimated from the data using linear functions.polyfit( x,y2,1) %return 2.1667 -1.3333, i.e 2.1667x-1.3333
26. When You Are Creating A Statistical Model How Do You Prevent Over-fitting?
Over-fitting can be prevented by cross-validation.
27. What Is Descriptive Statistics?
We study in descriptive statistics the methods for organizing, displaying, and describing data.
28. What Is A Sample?
When data are collected in a statistical study for only a portion or subset of all elements of interest we are using a Sample.
29. Give An Example Of Inferential Statistics?
Example of Inferential Statistic :You asked five of your classmates about their height. On the basis of this information, you stated that the average height of all students in your university or college is 67 inches.
30. A Normal Population Distribution Is Needed For The Which Of The Statistical Tests:
- variance estimation.
- standard error of the mean.
- Student’s t-test.
31. What are the types of sampling in Statistics?
There are four main types of data sampling as shown below:
- Simple random: Pure random division
- Cluster: Population divided into clusters
- Stratified: Data divided into unique groups
- Systematical: Picks up every ‘n’ member in the data
32. What is the meaning of covariance?
Covariance is the measure of indication when two items vary together in a cycle. The systematic relation is determined between a pair of random variables to see if the change in one will affect the other variable in the pair or not.
33. Imagine that Jeremy took part in an examination. The test is having a mean score of 160, and it has a standard deviation of 15. If Jeremy’s z-score is 1.20, what would be his score on the test?
To determine the solution to the problem, the following formula is used:
X = μ + Zσ
Here:
μ: Mean
σ: Standard deviation
X: Value to be calculated
Therefore, X = 160 + (15*1.2) = 173.8 (Approximated to 174)
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34. If a distribution is skewed to the right and has a median of 20, will the mean be greater than or less than 20?
If the given distribution is a right-skewed distribution, then the mean should be greater than 20, while the mode remains to be less than 20.
35. What is Bessel’s correction?
Bessel’s correction is a factor that is used to estimate a populations’ standard deviation from its sample. It causes the standard deviation to be less biased, thereby, providing more accurate results.
36. The standard normal curve has a total area to be under one, and it is symmetric around zero. True or False?
True, a normal curve will have the area under unity and the symmetry around zero in any distribution. Here, all of the measures of central tendencies are equal to zero due to the symmetric nature of the standard normal curve.
37. In an observation, there is a high correlation between the time a person sleeps and the amount of productive work he does. What can be inferred from this?
First, correlation does not imply causation here. Correlation is only used to measure the relationship, which is linear between rest and productive work. If both vary rapidly, then it means that there is a high amount of correlation between them.
38. What is the relationship between the confidence level and the significance level in statistics?
The significance level is the probability of obtaining a result that is extremely different from the condition where the null hypothesis is true. While the confidence level is used as a range of similar values in a population.
Both significance and confidence level are related by the following formula:
Significance level = 1 − Confidence level
39. A regression analysis between apples (y) and oranges (x) resulted in the following least-squares line: y = 100 + 2x. What is the implication if oranges are increased by 1?
If the oranges are increased by one, there will be an increase of 2 apples since the equation is:
y = 100 + 2x.
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40. What types of variables are used for Pearson’s correlation coefficient?
Variables to be used for the Pearson’s correlation coefficient must be either in a ratio or in an interval.
Note that there can exist a condition when one variable is a ratio, while the other is an interval score.
41. In a scatter diagram, what is the line that is drawn above or below the regression line called?
The line that is drawn above or below the regression line in a scatter diagram is called the residual or also the prediction error.
42. What are the examples of symmetric distribution?
Symmetric distribution means that the data on the left side of the median is the same as the one present on the right side of the median.
There are many examples of symmetric distribution, but the following three are the most widely used ones:
- Uniform distribution
- Binomial distribution
- Normal distribution
43. Where is inferential statistics used?
Inferential statistics is used for several purposes, such as research, in which we wish to draw conclusions about a population using some sample data. This is performed in a variety of fields, ranging from government operations to quality control and quality assurance teams in multinational corporations.
44. What is the relationship between mean and median in a normal distribution?
In a normal distribution, the mean is equal to the median. To know if the distribution of a dataset is normal, we can just check the dataset’s mean and median.
45. What is the difference between the Ist quartile, the IInd quartile, and the IIIrd quartile?
Quartiles are used to describe the distribution of data by splitting data into three equal portions, and the boundary or edge of these portions are called quartiles.
That is,
- The lower quartile (Q1) is the 25th percentile.
- The middle quartile (Q2), also called the median, is the 50th percentile.
- The upper quartile (Q3) is the 75th percentile.
46. How do the standard error and the margin of error relate?
The standard error and the margin of error are quite closely related to each other. In fact, the margin of error is calculated using the standard error. As the standard error increases, the margin of error also increases.
47. What is one sample t-test?
This T-test is a statistical hypothesis test in which we check if the mean of the sample data is statistically or significantly different from the population’s mean.
48. What is an alternative hypothesis?
The alternative hypothesis (denoted by H1) is the statement that must be true if the null hypothesis is false. That is, it is a statement used to contradict the null hypothesis. It is the opposing point of view that gets proven right when the null hypothesis is proven wrong.
49. Given a left-skewed distribution that has a median of 60, what conclusions can we draw about the mean and the mode of the data?
Given that it is a left-skewed distribution, the mean will be less than the median, i.e., less than 60, and the mode will be greater than 60.
50. What are the types of biases that we encounter while sampling?
Sampling biases are errors that occur when taking a small sample of data from a large population as the representation in statistical analysis. There are three types of biases:
The selection bias
The survivorship bias
The undercoverage bias
Next up on this top Statistics Interview Questions and answers blog, let us take a look at the advanced set of questions.
51. What are the scenarios where outliers are kept in the data?
There are not many scenarios where outliers are kept in the data, but there are some important situations when they are kept. They are kept in the data for analysis if:
- Results are critical
- Outliers add meaning to the data
- The data is highly skewed
52. Briefly explain the procedure to measure the length of all sharks in the world.
Following steps can be used to determine the length of sharks:
Define the confidence level (usually around 95%)
Use sample sharks to measure
Calculate the mean and standard deviation of the lengths
Determine t-statistics values
Determine the confidence interval in which the mean length lies
53. How does the width of the confidence interval change with length?
The width of the confidence interval is used to determine the decision-making steps. As the confidence level increases, the width also increases.
The following also apply:
Wide confidence interval: Useless information
Narrow confidence interval: High-risk factor
54. What is the meaning of degrees of freedom (DF) in statistics?
Degrees of freedom or DF is used to define the number of options at hand when performing an analysis. It is mostly used with t-distribution and not with the z-distribution.
If there is an increase in DF, the t-distribution will reach closer to the normal distribution. If DF > 30, this means that the t-distribution at hand is having all of the characteristics of a normal distribution.
55. How can you calculate the p-value using MS Excel?
Following steps are performed to calculate the p-value easily:
Find the Data tab above
Click on Data Analysis
Select Descriptive Statistics
Select the corresponding column
Input the confidence level
56. What is the law of large numbers in statistics?
The law of large numbers in statistics is a theory that states that the increase in the number of trials performed will cause a positive proportional increase in the average of the results becoming the expected value.
Example: The probability of flipping a fair coin and landing heads is closer to 0.5 when it is flipped 100,000 times when compared to 100 flips.
57. What are some of the properties of a normal distribution?
A normal distribution, regardless of its size, will have a bell-shaped curve that is symmetric along the axes.
Following are some of the important properties:
Unimodal: It has only one mode.
Symmetrical: Left and right halves of the curve are mirrored.
Central tendency: The mean, median, and mode are at the midpoint.
58. If there is a 30 percent probability that you will see a supercar in any 20-minute time interval, what is the probability that you see at least one supercar in the period of an hour (60 minutes)?
The probability of not seeing a supercar in 20 minutes is:
= 1 − P(Seeing one supercar)
= 1 − 0.3
= 0.7
Probability of not seeing any supercar in the period of 60 minutes is:
= (0.7) ^ 3 = 0.343
Hence, the probability of seeing at least one supercar in 60 minutes is:
= 1 − P(Not seeing any supercar)
= 1 − 0.343 = 0.657
59. What is the meaning of sensitivity in statistics?
Sensitivity, as the name suggests, is used to determine the accuracy of a classifier (logistic, random forest, etc.):
The simple formula to calculate sensitivity is:
Sensitivity = Predicted True Events/Total number of Events
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60. What are the types of biases that you can encounter while sampling?
There are three types of biases:
- Selection bias
- Survivorship bias
- Under coverage bias
61. What is the meaning of TF/IDF vectorization?
TF-IDF is an acronym for Term Frequency – Inverse Document Frequency. It is used as a numerical measure to denote the importance of a word in a document. This document is usually called the collection or the corpus.
The TF-IDF value is directly proportional to the number of times a word is repeated in a document. TF-IDF is vital in the field of Natural Language Processing (NLP) as it is mostly used in the domain of text mining and information retrieval.
62. What are some of the low and high-bias Machine Learning algorithms?
There are many low and high-bias Machine Learning algorithms, and the following are some of the widely used ones:
- Low bias: SVM, decision trees, KNN algorithm, etc.
- High bias: Linear and logistic regression
63. What is the use of Hash tables in statistics?
Hash tables are the data structures that are used to denote the representation of key-value pairs in a structured way. The hashing function is used by a hash table to compute an index that contains all of the details regarding the keys that are mapped to their associated values.
64. What are some of the techniques to reduce underfitting and overfitting during model training?
Underfitting refers to a situation where data has high bias and low variance, while overfitting is the situation where there are high variance and low bias.
Following are some of the techniques to reduce underfitting and overfitting:
For reducing underfitting:
- Increase model complexity
- Increase the number of features
- Remove noise from the data
- Increase the number of training epochs
For reducing overfitting:
- Increase training data
- Stop early while training
- Lasso regularization
- Use random dropouts
65. Can you give an example to denote the working of the central limit theorem?
Let’s consider the population of men who have normally distributed weights, with a mean of 60 kg and a standard deviation of 10 kg, and the probability needs to be found out.
If one single man is selected, the weight is greater than 65 kg, but if 40 men are selected, then the mean weight is far more than 65 kg.
The solution to this can be as shown below:
Z = (x − µ) / ? = (65 − 60) / 10 = 0.5
For a normal distribution P(Z > 0.5) = 0.409
Z = (65 − 60) / 5 = 1
P(Z > 1) = 0.090
66. How do you stay up-to-date with the new and upcoming concepts in statistics?
This is a commonly asked question in a statistics interview. Here, the interviewer is trying to assess your interest and ability to find out and learn new things efficiently. Do talk about how you plan to learn new concepts and make sure to elaborate on how you practically implemented them while learning.
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67. What is the benefit of using box plots?
Box plots allow us to provide a graphical representation of the 5-number summary and can also be used to compare groups of histograms.
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68. Does a symmetric distribution need to be unimodal?
A symmetric distribution does not need to be unimodal (having only one mode or one value that occurs most frequently). It can be bi-modal (having two values that have the highest frequencies) or multi-modal (having multiple or more than two values that have the highest frequencies).
69. What is the impact of outliers in statistics?
Outliers in statistics have a very negative impact as they skew the result of any statistical query. For example, if we want to calculate the mean of a dataset that contains outliers, then the mean calculated will be different from the actual mean (i.e., the mean we will get once we remove the outliers).
70. When creating a statistical model, how do we detect overfitting?
Overfitting can be detected by cross-validation. In cross-validation, we divide the available data into multiple parts and iterate on the entire dataset. In each iteration, one part is used for testing, and others are used for training. This way, the entire dataset will be used for training and testing purposes, and we can detect if the data is being overfitted.
71. What is a survivorship bias?
The survivorship bias is the flaw of the sample selection that occurs when a dataset only considers the ‘surviving’ or existing observations and fails to consider those observations that have already ceased to exist.
72. What is an undercoverage bias?
The undercoverage bias is a bias that occurs when some members of the population are inadequately represented in the sample.
73. What is the relationship between standard deviation and standard variance?
Standard deviation is the square root of standard variance. Basically, standard deviation takes a look at how the data is spread out from the mean. On the other hand, standard variance is used to describe how much the data varies from the mean of the entire dataset.