Statistics for Data Science: Learn via 700+ MCQs Quiz [2023]

Statistics for Data Science Mastery: Descriptive & Inferential Stats, Probability, Regression, ANOVA & More via 700+ MCQ

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Statistics for Data Science: Learn via 700+ MCQs Quiz – Updated on July 2023

Master the vital skill of Statistics for Data Science through our comprehensive quiz-based course. Engage, learn, and test your knowledge with 700+ Statistics for Data Science Multiple Choice Questions.

In the fast-paced world of data science, mastering statistics is crucial. Our course, Statistics for Data Science: Learn via 700+ MCQs Quiz, has been meticulously designed to equip you with the essential statistical knowledge required to thrive in the data science landscape.

This course isn’t your typical lecture-style class. Instead, we’ve developed a unique, interactive format focused on learning through multiple-choice questions. We believe the best way to understand and internalize “statistics for data science” is by continually testing and applying your knowledge. And what better way to do so than via a vast repository of 700+ MCQs?

What You Will Learn:

1. Section 1: Descriptive Statistics

   • Introduction to Statistics

   • Types of Data: Quantitative vs. Qualitative

   • Measures of Central Tendency (Mean, Median, Mode)

   • Measures of Dispersion (Range, Variance, Standard Deviation)

   • Measures of Shape (Skewness and Kurtosis)

   • Understanding Distributions (Uniform, Normal, Skewed)

   • Data Visualization: Box plots, Histograms, and Bar Plots

2. Section 2: Probability Theory

   • Basics of Probability (Experiments, Outcomes, Events)

   • Rules of Probability (Addition and Multiplication Rules)

   • Conditional Probability and Independence

   • Bayes’ Theorem

   • Random Variables and Probability Distributions (Discrete and Continuous)

   • Special Distributions (Uniform, Binomial, Normal, Poisson)

   • Central Limit Theorem and Law of Large Numbers

3. Section 3: Inferential Statistics

   • Sampling and Sampling Distributions

   • Point and Interval Estimation

   • Confidence Intervals for Mean and Proportions

   • Hypothesis Testing Basics (Null and Alternative Hypotheses)

   • Z-tests and T-tests for Means

   • Chi-square Tests for Independence

   • Understanding Errors in Hypothesis Testing (Type I and Type II Errors, Power of a Test)

4. Section 4: Correlation and Regression

   • Scatter Plots and Correlation

   • Pearson’s Correlation Coefficient

   • Simple Linear Regression (Assumptions, Estimation, Inference)

   • Residual Analysis and Diagnostics in Simple Linear Regression

   • Multiple Linear Regression

   • Inference in Multiple Linear Regression

   • Multicollinearity and Model Selection in Multiple Regression

5. Section 5: Multivariate Analysis

   • Extensions of Regression Analysis (Polynomial Regression, Interaction Effects)

   • Introduction to Analysis of Variance (ANOVA)

   • One-way and Two-way ANOVA

   • Principal Component Analysis (PCA)

   • Factor Analysis

   • Cluster Analysis

6. Section 6: Non-parametric Tests

   • Introduction to Non-parametric Statistics

   • Sign Test and Wilcoxon Signed Rank Test

   • Mann-Whitney U Test

   • Kruskal-Wallis Test

   • Spearman’s Rank Correlation

   • Chi-square Test for Goodness of Fit

Here are some example MCQs for the sections mentioned.

Section 1: Descriptive Statistics

1. Introduction to Statistics

Q1: In the context of statistics for data science, which of the following best describes the purpose of statistics?

• A. Only to gather data

• B. Only to present data visually

• C. To make predictions about future trends

• D. To make the computer run faster

Correct Option: C.

Explanation: In “statistics for data science”, the main goal of statistics is not merely to gather or present data but to analyze it in order to make informed decisions, predictions about future trends, and interpret complex data sets.

2. Types of Data: Quantitative vs. Qualitative

Q2: Which type of data is best suited for a pie chart visualization in statistics for data science?

• A. Continuous Quantitative Data

• B. Discrete Quantitative Data

• C. Nominal Qualitative Data

• D. Ordinal Quantitative Data

Correct Option: C.

Explanation: In statistics for data science, nominal qualitative data, which refers to non-numerical data that can be categorized, is often best visualized using a pie chart. The pie chart clearly shows the proportion of each category in the total.

3. Measures of Central Tendency (Mean, Median, Mode)

Q3: Which measure of central tendency is not affected by outliers in statistics for data science?

• A. Mean

• B. Mode

• C. Median

• D. All are affected by outliers

Correct Option: C.

Explanation: In statistics for data science, the median, which is the middle value of a data set when ordered, is not affected by extreme values (outliers), unlike the mean. The mode, representing the most common value in a data set, can potentially be influenced by outliers if they occur frequently.

4. Measures of Dispersion (Range, Variance, Standard Deviation)

Q4: Which measure of dispersion is most affected by outliers in statistics for data science?

• A. Range

• B. Variance

• C. Standard Deviation

• D. Coefficient of Variation

Correct Option: A.

Explanation: In “statistics for data science”, the range, which is calculated as the difference between the largest and the smallest data point in the dataset, is most affected by outliers as it only considers these two points and not the overall data distribution.

5. Measures of Shape (Skewness and Kurtosis)

Q5: In statistics for data science, a distribution is considered “positively skewed” if…?

• A. The tail is longer on the left side

• B. The tail is longer on the right side

• C. It is a normal distribution

• D. The distribution has no tail

Correct Option: B.

Explanation: In “statistics for data science”, a distribution is said to be positively skewed if the tail on the right side (larger end of the distribution) is longer. This means that a few data points are significantly larger than the rest.

6. Understanding Distributions (Uniform, Normal, Skewed)

Q6: Which of the following distributions has a bell-shaped curve in statistics for data science?

• A. Uniform Distribution

• B. Skewed Distribution

• C. Normal Distribution

• D. None of the above

Correct Option: C.

Explanation: In statistics for data science, a normal distribution, also known as a Gaussian distribution, has a bell-shaped curve. It is symmetrical around the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean.

7. Data Visualization: Box plots, Histograms, and Bar Plots

Q7: In statistics for data science, which of the following visualizations can be used to identify outliers?

• A. Bar plot

• B. Pie chart

• C. Line graph

• D. Box plot

Correct Option: D.

Explanation: In “statistics for data science”, box plots are an excellent tool for identifying outliers. They represent the interquartile range (where most of the data lie) and any data point outside this range (represented by ‘whiskers’) is considered an outlier.

Section 2: Probability Theory

1. Basics of Probability (Experiments, Outcomes, Events)

Q1: In statistics for data science, what does an ‘event’ refer to in the context of probability?

• A. An experiment

• B. An outcome

• C. A set of outcomes

• D. None of the above

Correct Option: C.

Explanation: In statistics for data science, an ‘event’ in the context of probability refers to a set of outcomes from the sample space. An event may consist of one outcome, multiple outcomes, or even no outcome.

2. Rules of Probability (Addition and Multiplication Rules)

Q2: In statistics for data science, when is the addition rule of probability used?

• A. To calculate the probability of the intersection of two events

• B. To calculate the probability of the union of two events

• C. To calculate the conditional probability of an event

• D. To calculate the inverse probability of an event

Correct Option: B.

Explanation: In statistics for data science, the addition rule of probability is used to calculate the probability of the union of two events (i.e., the probability that either of the two events happens).

3. Conditional Probability and Independence

Q3: In statistics for data science, if two events are independent, the probability of both occurring is given by…?

• A. The sum of their individual probabilities

• B. The difference of their individual probabilities

• C. The product of their individual probabilities

• D. None of the above

Correct Option: C.

Explanation: In statistics for data science, if two events are independent, then the probability of both events occurring is the product of the probabilities of each event.

4. Bayes’ Theorem

Q4: In statistics for data science, Bayes’ Theorem is often used to…?

• A. Calculate the mean of a dataset

• B. Predict future events

• C. Update prior probabilities given new data

• D. Establish causality between variables

Correct Option: C.

Explanation: In statistics for data science, Bayes’ theorem is often used to update prior probabilities given new data. This theorem forms the basis of Bayesian inference, where the probability of a hypothesis is updated as more evidence or information becomes available.

5. Random Variables and Probability Distributions (Discrete and Continuous)

Q5: In statistics for data science, which of the following can be represented by a continuous random variable?

• A. The number of students in a class

• B. The roll of a die

• C. The height of a person

• D. The number of tails in 3 coin flips

Correct Option: C.

Explanation: In statistics for data science, the height of a person can be represented by a continuous random variable, as it can take on any value within a specified range and is not just limited to distinct separate values.

6. Special Distributions (Uniform, Binomial, Normal, Poisson)

Q6: In statistics for data science, which distribution would be most appropriate to model the number of emails arriving in your inbox in a given hour?

• A. Uniform Distribution

• B. Binomial Distribution

• C. Normal Distribution

• D. Poisson Distribution

Correct Option: D.

Explanation: In statistics for data science, the Poisson distribution would be most appropriate to model the number of emails arriving in your inbox in a given hour. The Poisson distribution models the number of events (in this case, emails) occurring in a fixed interval of time.

7. Central Limit Theorem and Law of Large Numbers

Q7: In statistics for data science, the Central Limit Theorem is important because it…?

• A. Ensures that data is normally distributed

• B. Allows us to use normal distribution approximations for large datasets

• C. States that the sum of a number of random variables behaves like a normal distribution

• D. All of the above

Correct Option: D.

Explanation: In statistics for data science, the Central Limit Theorem is important for all of the reasons listed above. It states that the sum or average of a large number of independent and identically distributed random variables, no matter the original distribution, approaches a normal distribution. This allows us to make predictions about large datasets using the normal distribution approximation.

Section 3: Inferential Statistics

1. Sampling and Sampling Distributions

Q1: In statistics for data science, which sampling method ensures every member of the population has an equal chance of being selected?

• A. Stratified Sampling

• B. Cluster Sampling

• C. Simple Random Sampling

• D. Convenience Sampling

Correct Option: C.

Explanation: In statistics for data science, Simple Random Sampling ensures that every member of the population has an equal chance of being selected. This type of sampling is akin to a random lottery draw where each ticket (i.e., each population member) has an equal chance of being drawn.

2. Point and Interval Estimation

Q2: In statistics for data science, what does a confidence interval estimate?

• A. The precise value of the population parameter

• B. The likely range of values of the population parameter

• C. The variance of the population

• D. The size of the sample needed for a study

Correct Option: B.

Explanation: In statistics for data science, a confidence interval provides an estimated range of values which is likely to include an unknown population parameter. The width of the confidence interval gives us an idea about how uncertain we are about the unknown parameter.

3. Confidence Intervals for Mean and Proportions

Q3: In statistics for data science, if we want to increase the confidence level of an interval estimate, what happens to the width of the confidence interval?

• A. It gets narrower

• B. It stays the same

• C. It gets wider

• D. It becomes zero

Correct Option: C.

Explanation: In statistics for data science, when we increase the confidence level, the width of the confidence interval gets wider. This happens because to be more confident that we’ve captured the true population parameter, we need to consider a wider range of values.

4. Hypothesis Testing Basics (Null and Alternative Hypotheses)

Q4: In the context of statistics for data science, which of the following best describes a null hypothesis?

• A. It is the hypothesis we want to prove.

• B. It is always the negative outcome.

• C. It is the hypothesis that there is no effect or relationship.

• D. It is the alternative to the primary hypothesis.

Correct Option: C.

Explanation: In statistics for data science, the null hypothesis is the hypothesis that there is no effect or relationship between variables. In a statistical test, this hypothesis is assumed to be true until evidence suggests otherwise.

5. Z-tests and T-tests for Means

Q5: In statistics for data science, when should you use a t-test instead of a z-test?

• A. When the population variance is known.

• B. When the population variance is unknown.

• C. When the sample size is over 30.

• D. Always use a z-test.

Correct Option: B.

Explanation: In statistics for data science, a t-test is used when the population variance is unknown, and the sample size is small (typically under 30). The t-distribution is more spread out and has fatter tails than the z-distribution, which makes it more adaptable to uncertainty about the variance.

6. Chi-square Tests for Independence

Q6: In statistics for data science, a Chi-square test for independence is used to determine whether…?

• A. Two categorical variables are related in some population.

• B. Two numerical variables are related in some population.

• C. A single categorical variable is related to itself in some population.

• D. A single numerical variable is related to itself in some population.

Correct Option: A.

Explanation: In statistics for data science, a Chi-square test for independence is used to determine whether two categorical variables are related in some population. It is a non-parametric test that is used to determine if there is a significant association between two nominal (categorical) variables.

7. Understanding Errors in Hypothesis Testing (Type I and Type II Errors, Power of a Test)

Q7: In the context of statistics for data science, which type of error occurs if you reject a true null hypothesis?

• A. Type I error

• B. Type II error

• C. Both Type I and Type II errors

• D. Neither Type I nor Type II error

Correct Option: A.

Explanation: In statistics for data science, a Type I error occurs if you reject a true null hypothesis. This is equivalent to a false positive result – we have identified an effect or difference when actually there is none (i.e., the null hypothesis was true).

Section 4: Correlation and Regression

1. Scatter Plots and Correlation

Q1: In statistics for data science, what is a scatter plot primarily used for?

• A. To compare the means of two data sets

• B. To visualize the relationship between two numerical variables

• C. To visualize the distribution of a single numerical variable

• D. To compare the medians of two data sets

Correct Option: B.

Explanation: In statistics for data science, a scatter plot is primarily used to visualize the relationship between two numerical variables. By plotting each data point, we can get a visual sense of how one variable changes relative to changes in the other variable.

2. Pearson’s Correlation Coefficient

Q2: In statistics for data science, Pearson’s Correlation Coefficient is used to measure what kind of relationship between two variables?

• A. Nonlinear relationship

• B. Linear relationship

• C. Quadratic relationship

• D. Exponential relationship

Correct Option: B.

Explanation: In statistics for data science, Pearson’s Correlation Coefficient is used to measure the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

3. Simple Linear Regression (Assumptions, Estimation, Inference)

Q3: In statistics for data science, which of the following is not an assumption of simple linear regression?

• A. Linearity

• B. Homoscedasticity

• C. Independence of observations

• D. All variables follow a normal distribution

Correct Option: D.

Explanation: In statistics for data science, simple linear regression makes several assumptions, including linearity (the relationship between independent and dependent variable is linear), homoscedasticity (constant variance of errors), and independence of observations. However, it doesn’t assume that all variables must follow a normal distribution.

4. Residual Analysis and Diagnostics in Simple Linear Regression

Q4: In statistics for data science, what is a ‘residual’ in the context of a simple linear regression?

• A. The coefficient of the independent variable

• B. The predicted value of the dependent variable

• C. The difference between the observed and predicted values of the dependent variable

• D. The correlation between the independent and dependent variables

Correct Option: C.

Explanation: In statistics for data science, a ‘residual’ in the context of a simple linear regression is the difference between the observed and predicted values of the dependent variable. It represents the error or the part of the dependent variable that is not explained by the model.

5. Multiple Linear Regression

Q5: In statistics for data science, what is the main difference between simple linear regression and multiple linear regression?

• A. Simple linear regression uses one independent variable, while multiple linear regression uses two or more independent variables.

• B. Simple linear regression can handle categorical variables, while multiple linear regression cannot.

• C. Simple linear regression uses one dependent variable, while multiple linear regression uses two or more dependent variables.

• D. Simple linear regression cannot handle interactions between variables, while multiple linear regression can.

Correct Option: A.

Explanation: In statistics for data science, the primary difference between simple linear regression and multiple linear regression is the number of independent variables. Simple linear regression uses one independent variable to predict a dependent variable, while multiple linear regression uses two or more independent variables to predict a dependent variable.

6. Inference in Multiple Linear Regression

Q6: In statistics for data science, which statistical test is most commonly used to evaluate the overall fit of a multiple linear regression model?

• A. T-test

• B. Z-test

• C. Chi-square test

• D. F-test

Correct Option: D.

Explanation: In statistics for data science, the F-test is most commonly used to evaluate the overall fit of a multiple linear regression model. The F-test can determine if the variances in the residuals are due to the variables we have included in our model or due to unexplained variability.

7. Multicollinearity and Model Selection in Multiple Regression

Q7: In statistics for data science, which issue can arise in multiple linear regression when two or more independent variables are highly correlated?

• A. Underfitting

• B. Overfitting

• C. Multicollinearity

• D. Heteroscedasticity

Correct Option: C.

Explanation: In statistics for data science, multicollinearity can occur in multiple linear regression when two or more independent variables are highly correlated. This can cause problems as it undermines the statistical significance of an independent variable, and it makes the model’s estimates and predictions less reliable.

Section 5: Multivariate Analysis

1. Extensions of Regression Analysis (Polynomial Regression, Interaction Effects)

Q1: In statistics for data science, what is the primary difference between simple linear regression and polynomial regression?

• A. Simple linear regression can handle multiple independent variables, while polynomial regression cannot.

• B. Simple linear regression uses linear equations, while polynomial regression uses polynomial equations.

• C. Simple linear regression can handle interaction effects, while polynomial regression cannot.

• D. Simple linear regression is a type of multivariate analysis, while polynomial regression is not.

Correct Option: B.

Explanation: In statistics for data science, the main difference between simple linear regression and polynomial regression is the type of equation they use. Simple linear regression uses linear equations to model relationships, while polynomial regression uses polynomial equations, allowing for more complex relationships between independent and dependent variables.

2. Introduction to Analysis of Variance (ANOVA)

Q2: In statistics for data science, what does an ANOVA test primarily determine?

• A. If the means of two populations are equal

• B. If the variances of two populations are equal

• C. If the means of three or more independent groups are equal

• D. If the variances of three or more independent groups are equal

Correct Option: C.

Explanation: In statistics for data science, Analysis of Variance (ANOVA) primarily determines if there are any statistically significant differences between the means of three or more independent groups. It achieves this by examining the variance within each group and the variance between groups.

3. One-way and Two-way ANOVA

Q3: In statistics for data science, what is the difference between one-way and two-way ANOVA?

• A. One-way ANOVA tests for differences in one independent variable, while two-way ANOVA tests for differences in two independent variables.

• B. One-way ANOVA is used with continuous data, while two-way ANOVA is used with categorical data.

• C. One-way ANOVA is a non-parametric test, while two-way ANOVA is a parametric test.

• D. One-way ANOVA can be used with paired samples, while two-way ANOVA cannot.

Correct Option: A.

Explanation: In statistics for data science, one-way ANOVA is used to test for differences among at least three groups, based on one independent variable (factor). Two-way ANOVA is an extension of the one-way ANOVA that allows for the examination of the effects of two independent variables (factors) on a dependent variable.

4. Principal Component Analysis (PCA)

Q4: In statistics for data science, what is the primary use of Principal Component Analysis (PCA)?

• A. To classify categorical data into different groups

• B. To reduce the dimensionality of the dataset while retaining as much information as possible

• C. To find the linear regression line that best fits the data

• D. To compare the means of three or more groups

Correct Option: B.

Explanation: In statistics for data science, Principal Component Analysis (PCA) is primarily used to reduce the dimensionality of the dataset while retaining as much information as possible. This technique transforms a large set of variables into a smaller one that still contains most of the information in the large set.

5. Factor Analysis

Q5: In statistics for data science, what is the main objective of Factor Analysis?

• A. To classify data into clusters based on their similarity

• B. To identify underlying variables (factors) that explain the pattern of correlations within a set of observed variables

• C. To test if the means of two populations are equal

• D. To reduce the dimensionality of a dataset

Correct Option: B.

Explanation: In statistics for data science, the main objective of Factor Analysis is to identify underlying variables (factors) that explain the pattern of correlations within a set of observed variables. It is a technique used to reduce a large number of variables into fewer numbers of factors.

6. Cluster Analysis

Q6: In statistics for data science, what is the primary purpose of Cluster Analysis?

• A. To identify underlying factors in a dataset

• B. To classify observations into groups (clusters) based on their similarity across several dimensions

• C. To test if the means of three or more groups are equal

• D. To predict a dependent variable based on one or more independent variables

Correct Option: B.

Explanation: In statistics for data science, the primary purpose of Cluster Analysis is to classify observations into groups (clusters) based on their similarity across several dimensions. These clusters should maximise the similarity of observations within each group and maximise the dissimilarity between groups.

Section 6: Non-parametric Tests

1. Introduction to Non-parametric Statistics

Q1: In statistics for data science, when would you typically choose to use non-parametric statistical tests?

• A. When data follow a normal distribution

• B. When data do not meet the assumptions of parametric tests

• C. When data are continuous and linear

• D. When data have a large sample size

Correct Option: B.

Explanation: In statistics for data science, non-parametric statistical tests are typically used when the data do not meet the assumptions of parametric tests, such as normality or homoscedasticity. Non-parametric tests are more flexible and can be used with ordinal, nominal, and ranked data, and when the sample size is small.

2. Sign Test and Wilcoxon Signed Rank Test

Q2: In statistics for data science, what are the Sign Test and Wilcoxon Signed Rank Test primarily used for?

• A. To compare the medians of two independent samples

• B. To compare the means of two independent samples

• C. To compare the median of a single sample to a hypothesized value

• D. To test for a linear relationship between two variables

Correct Option: C.

Explanation: In statistics for data science, the Sign Test and Wilcoxon Signed Rank Test are non-parametric tests primarily used to compare the median of a single sample to a hypothesized value. They can also be used for paired samples to test if the distributions of the two samples are the same.

3. Mann-Whitney U Test

Q3: In statistics for data science, when is the Mann-Whitney U Test typically used?

• A. When comparing the means of two independent samples

• B. When comparing the medians of two independent samples

• C. When comparing the variance of two independent samples

• D. When testing for a linear relationsh

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