[100+] Statistics MCQs & Answers {PDF} For NTS, NET, SSB, SSC, IBPS, RRB, Govt. Exams

1. Standard Deviation
2. Range
3. Median
4. Variance

Ans. C

The median is a measure of central tendency that represents the middle value of a dataset when arranged in ascending order.

1. Sum of data values / Number of data points
2. Standard Deviation / Mean
3. (Sum of squared differences from the mean) / Number of data points
4. Median / Range

Ans. C

The variance is calculated by taking the sum of the squared differences of each data point from the mean and then dividing it by the number of data points.

1. The power of the test
2. The significance level of the test
3. The probability of observing the data or more extreme data under the null hypothesis
4. The confidence interval of the test

Ans. C

The p-value represents the probability of observing the data or more extreme data under the null hypothesis, indicating the strength of evidence against the null hypothesis.

1. To show the distribution of data and identify outliers
2. To display the frequency distribution of data
3. To represent the relationship between two variables
4. To compare means of different data sets

Ans. A

A box plot is used to visualize the distribution of data, including the identification of outliers and the spread of the data.

1. (Sum of products of deviations from means) / (Product of standard deviations)
2. (Sum of squared deviations from means) / (Product of means)
3. (Sum of squared deviations from means) / (Product of standard deviations)
4. (Sum of products of deviations from means) / (Sum of squared deviations from means)

Ans. A

The formula for Pearson’s correlation coefficient (r) involves the sum of products of deviations from means divided by the product of standard deviations of the two variables.

1. Mean
2. Median
3. Range
4. Mode

Ans. C

The range measures the spread or variability of data in a data set, calculated as the difference between the maximum and minimum values.

1. Normal distribution
2. Poisson distribution
3. Binomial distribution
4. Exponential distribution

Ans. B

The Poisson distribution is used to model the number of events occurring within a fixed interval when events are rare and independent.

1. Analysis of Variability
2. Analysis of Varying Outcomes
3. Analysis of Variance
4. Association of Variables

Ans. C

ANOVA stands for “Analysis of Variance,” a statistical technique used to analyze the variance between groups in a dataset.

1. To determine the sample size required for an experiment
2. To estimate a population parameter with a range of values
3. To test the null hypothesis
4. To compare means of two groups

Ans. B

The primary purpose of a confidence interval is to provide an estimate of a population parameter along with a range of values within which the parameter is likely to fall.

1. The measure of how spread out data values are
2. The measure of symmetry in a data distribution
3. The measure of central tendency
4. The measure of variability

Ans. B

Skewness measures the degree of symmetry or asymmetry in a data distribution. Positive skew indicates a tail on the right, and negative skew indicates a tail on the left.

1. 0.05
2. 0.01
3. 0.10
4. 0.50

Ans. A

For a two-tailed test at a 95% confidence level, the significance level is often set at 0.05, meaning there is a 5% chance of making a Type I error.

1. Range
2. Mean Absolute Deviation (MAD)
3. Variance
4. Interquartile Range (IQR)

Ans. D

The Interquartile Range (IQR) is less sensitive to extreme outliers because it is based on the middle 50% of the data and ignores extreme values.

1. T-test
2. Chi-squared test
3. ANOVA
4. Regression analysis

Ans. B

The Chi-squared test is used to determine if there is a significant relationship between two categorical variables by comparing observed and expected frequencies.

1. (Standard Deviation / Mean) × 100
2. (Range / Median) × 100
3. (Variance / Mode) × 100
4. (Mean Absolute Deviation / Range) × 100

Ans. A

The coefficient of variation (CV) is calculated by dividing the standard deviation by the mean and multiplying the result by 100.

1. The probability of making a Type II error
2. The probability of observing the null hypothesis being true
3. The probability of obtaining the observed results by chance under the null hypothesis
4. The power of the test

Ans. C

The p-value represents the probability of obtaining the observed results by chance under the null hypothesis, and it helps assess the strength of evidence against the null hypothesis.

1. To compare two data sets
2. To show the distribution of categorical data
3. To display the relationship between two variables
4. To represent the frequency distribution of a continuous variable

Ans. D

A histogram is used to represent the frequency distribution of a continuous variable, showing how data is distributed across different values or intervals.

1. The mean of a dataset
2. Data points that are significantly different from the others
3. The median of a dataset
4. The range of a dataset

Ans. B

Outliers are data points that are significantly different from the majority of the data in a dataset and may skew statistical analysis.

1. Normal distribution
2. Poisson distribution
3. Binomial distribution
4. Exponential distribution

Ans. C

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials (experiments with two possible outcomes).

1. Alternative hypothesis
2. Null hypothesis
3. Two-tailed hypothesis
4. Significance hypothesis

Ans. B

The null hypothesis (H0) assumes no effect or relationship in a statistical test and is used for hypothesis testing.

1. Standard Deviation / Sample Size
2. Sample Size / Standard Deviation
3. Range / Mean
4. Variance / Median

Ans. A

The standard error of the mean (SEM) is calculated by dividing the standard deviation by the square root of the sample size.

1. Student’s t-test
2. Mann-Whitney U test
3. Analysis of Variance (ANOVA)
4. Chi-squared test

Ans. C

Analysis of Variance (ANOVA) is used to compare the means of three or more groups in a study to determine if there are statistically significant differences among them.

1. To compare means of two groups
2. To represent the frequency distribution of data
3. To display the relationship between two continuous variables
4. To show the distribution of categorical data

Ans. C

A scatter plot is used to display the relationship between two continuous variables, helping to identify patterns and correlations between them.

1. (Data Value – Mean) / Standard Deviation
2. (Data Value – Median) / Range
3. (Data Value – Variance) / Mean
4. (Data Value – Mode) / Sample Size

Ans. A

The z-score of a data point in a normal distribution is calculated by subtracting the mean from the data value and dividing by the standard deviation.

1. The null hypothesis is likely true
2. There is strong evidence against the null hypothesis
3. The significance level is 0.02
4. The test is inconclusive

Ans. B

A p-value of 0.02 indicates that there is strong evidence against the null hypothesis, and it is likely to be rejected.

1. The error made by the statistician during data collection
2. The difference between the sample statistic and the population parameter
3. The error introduced during data entry and analysis
4. The variation within the sample data

Ans. B

Sampling error is the difference between a sample statistic and the population parameter it estimates and is due to random sampling.

1. Student’s t-test
2. Chi-squared test
3. Wilcoxon signed-rank test
4. Analysis of Variance (ANOVA)

Ans. C

The Wilcoxon signed-rank test is a non-parametric test used for comparing two related groups or paired data when assumptions of parametric tests are not met.

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Negative Binomial distribution

Ans. D

The Negative Binomial distribution describes the number of successful Bernoulli trials before a specified number of failures occurs.

1. The level of significance in hypothesis testing
2. The likelihood that a sample is representative of the population
3. The range of values within which a parameter is estimated to fall
4. The proportion of a population captured by a sample

Ans. C

The confidence level represents the range of values within which a parameter is estimated to fall with a certain level of certainty, typically expressed as a percentage.

1. (Probability of the event) / (1 – Probability of the event)
2. (Probability of the event) × (1 – Probability of the event)
3. (Odds of the event) / (1 – Odds of the event)
4. (Odds of the event) × (1 – Odds of the event)

Ans. A

The probability of an event can be calculated from the odds ratio using the formula (Probability of the event) / (1 – Probability of the event).

1. The strength of a linear relationship between two variables
2. The difference between the mean and median of a dataset
3. The variability within a sample
4. The spread of data values in a dataset

Ans. A

Correlation measures the strength and direction of a linear relationship between two variables, indicating how one variable changes when the other changes.

1. Variance
2. Standard Deviation
3. Range
4. Mode

Ans. B

The standard deviation is a measure of how much data values tend to deviate from the mean in a dataset, indicating the spread or dispersion of data.

1. The probability of making a Type II error
2. The probability of observing the null hypothesis being true
3. The probability of obtaining the observed results by chance under the null hypothesis
4. The power of the test

Ans. C

The p-value represents the probability of obtaining the observed results by chance under the null hypothesis, helping assess the strength of evidence against the null hypothesis.

1. Range
2. Mean Absolute Deviation (MAD)
3. Variance
4. Interquartile Range (IQR)

Ans. D

The Interquartile Range (IQR) is a measure of the spread of data values around the median and is less affected by extreme outliers.

1. The standard deviation of a sample
2. The margin of error in a confidence interval
3. The mean of a population
4. The range of values in a data set

Ans. B

The standard error represents the margin of error in a confidence interval, indicating the precision of an estimate based on sample data.

1. Pearson’s correlation coefficient (r)
2. Spearman’s rank correlation (rho)
3. Chi-squared test
4. ANOVA

Ans. B

Spearman’s rank correlation (rho) is a measure of association used to assess the relationship between two ordinal variables by ranking their values.

1. Incorrectly rejecting a true null hypothesis
2. Incorrectly accepting a false null hypothesis
3. Correctly rejecting a false null hypothesis
4. Correctly accepting a true null hypothesis

Ans. A

A Type I error occurs when a true null hypothesis is incorrectly rejected, leading to a false positive result in hypothesis testing.

1. Outlier detection
2. Data transformation
3. Imputation
4. Sampling

Ans. C

Imputation is the method used to assign a value to missing data points based on other available data in a dataset, allowing for analysis with complete data.

1. Interquartile Range (IQR)
2. Variance
3. Standard Error
4. Coefficient of Variation

Ans. A

The Interquartile Range (IQR) is the range of values that separates the central 50% of data from the extreme values in a dataset and is a measure of data spread.

1. Chi-squared test
2. Two-sample t-test
3. Mann-Whitney U test
4. ANOVA

Ans. B

The two-sample t-test is used to determine if there is a significant difference in means between two independent groups or samples.

1. The measure of symmetry in a data distribution
2. The measure of central tendency
3. The measure of variability within a sample
4. The measure of the spread of data values

Ans. A

Skewness measures the symmetry or asymmetry in a data distribution. Positive skew indicates a right-skewed distribution, while negative skew indicates a left-skewed distribution.

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Binomial distribution

Ans. C

The exponential distribution is commonly used to model the time between events occurring at a constant rate or in a Poisson process.

1. Confidence interval
2. Type I error
3. P-value
4. Margin of error

Ans. C

The p-value is the likelihood of observing the data or more extreme data, assuming the null hypothesis is true, in a hypothesis test. A smaller p-value indicates stronger evidence against the null hypothesis.

1. Mean
2. Median
3. Mode
4. Range

Ans. A

The mean is the measure of central tendency most affected by outliers, as it takes all values into account when calculating the average.

1. Chi-squared test
2. Pearson’s correlation coefficient
3. Mann-Whitney U test
4. T-test

Ans. B

Pearson’s correlation coefficient is used to assess the strength and direction of the linear relationship between two continuous variables.

1. (Odds of the event) / (Odds against the event)
2. (Probability of the event) × (Probability against the event)
3. (Odds of the event) / (Probability of the event)
4. (Probability of the event) / (1 – Probability of the event)

Ans. A

The probability of an event can be calculated from odds using the formula (Odds of the event) / (Odds against the event).

1. Standard Deviation
2. Range
3. Variance
4. Dispersion

Ans. D

Dispersion is a measure of how data values tend to cluster around a central point, reflecting the degree of spread or concentration in the data.

1. A range of values within which a parameter is estimated to fall
2. The probability of making a Type I error
3. The strength of a linear relationship between two variables
4. The margin of error in a hypothesis test

Ans. A

A confidence interval represents a range of values within which a parameter is estimated to fall with a specified level of confidence.

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Binomial distribution

Ans. D

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, which are experiments with two possible outcomes.

1. The probability of making a Type I error
2. The probability of observing the null hypothesis being true
3. The probability of correctly rejecting the null hypothesis
4. The probability of obtaining extreme data by chance

Ans. C

Power represents the probability of correctly rejecting the null hypothesis when it is false, indicating the test’s ability to detect a true effect.

1. Scatter plot
2. Box plot
3. Bar chart
4. Frequency table

Ans. B

A box plot (box-and-whisker plot) is a graphical representation that displays the distribution, central tendency, and spread of a dataset.

1. Continuous data
2. Nominal data
3. Ordinal data
4. Discrete data

Ans. D

Discrete data is a type of data that can take on only specific, often whole number values, and is used to represent counts or categories.

1. Confidence interval
2. Sampling error
3. Type I error
4. Standard error

Ans. D

Standard error is a measure of the degree of uncertainty or variability associated with a statistic and indicates how much the sample statistic might vary from the population parameter.

1. Student’s t-test
2. Chi-squared test
3. Mann-Whitney U test
4. Analysis of Variance (ANOVA)

Ans. D

Analysis of Variance (ANOVA) is used to compare the means of three or more groups in a study to determine if there are statistically significant differences among them.

1. The range of data values
2. The strength and direction of a relationship between two variables
3. The probability of making a Type I error
4. The margin of error in a confidence interval

Ans. B

A correlation coefficient measures the strength and direction of a relationship between two variables, indicating how they are related to each other.

1. Standard deviation
2. Range
3. Interquartile range
4. Mode

Ans. A

Standard deviation is a measure of how data values are distributed around a central point, representing the degree of spread or dispersion in the data.

1. Skewness
2. Variance
3. Standard error
4. Mean absolute deviation (MAD)

Ans. B

Variance is a measure of how much data values tend to deviate from the mean in a dataset, indicating the degree of variability.

1. The probability of making a Type I error
2. The significance level or threshold for rejecting the null hypothesis
3. The p-value
4. The probability of correctly accepting the null hypothesis

Ans. B

The alpha level represents the significance level or threshold for rejecting the null hypothesis in hypothesis testing.

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Binomial distribution

Ans. C

The exponential distribution is used to model the time between events occurring at a constant rate or in a Poisson process.

1. Outlier detection
2. Feature selection
3. Imputation
4. Hypothesis testing

Ans. B

Feature selection is a method used to reduce the dimensionality of data while retaining as much relevant information as possible for analysis.

1. The number of data points in a dataset
2. The sample size
3. The number of groups in an ANOVA test
4. The number of values that are free to vary in a statistical calculation

Ans. D

Degrees of freedom refer to the number of values that are free to vary in a statistical calculation and play a role in various statistical tests.

1. The hypothesis that is proven to be true
2. The alternative hypothesis
3. The hypothesis to be rejected if evidence suggests otherwise
4. The initial assumption to be tested

Ans. D

The null hypothesis is the initial assumption to be tested in hypothesis testing, typically representing no effect or no difference.

1. Student’s t-test
2. Pearson’s chi-squared test
3. Wilcoxon signed-rank test
4. Analysis of Variance (ANOVA)

Ans. B

Pearson’s chi-squared test is used to assess the significant difference between observed and expected frequencies in a contingency table.

1. Simple random sampling
2. Cluster sampling
3. Stratified sampling
4. Convenience sampling

Ans. C

Stratified sampling is a method in which the population is divided into non-overlapping strata, and a random sample is taken from each stratum, ensuring representation from all groups.

1. Mean
2. Median
3. Mode
4. Range

Ans. C

The mode is a measure of central tendency used with nominal data and represents the most frequently occurring value in a dataset.

1. The level of significance in hypothesis testing
2. The likelihood that a sample is representative of the population
3. The range of values within which a parameter is estimated to fall
4. The proportion of a population captured by a sample

Ans. C

The confidence level in a confidence interval represents the range of values within which a parameter is estimated to fall with a specified level of confidence.

1. Central tendency
2. Variance
3. Standard error
4. Mode

Ans. B

Variance is the measure of how data values are spread out or dispersed in a dataset, indicating the degree of variability.

1. Probability
2. Causation
3. Correlation
4. Variance

Ans. C

Correlation is a statistical measure that describes the direction and strength of a relationship between two variables, indicating how they are related.

1. Skewness
2. Kurtosis
3. Central tendency
4. Spread

Ans. A

Skewness is a statistical measure that describes the symmetry or asymmetry of a probability distribution, indicating whether it is skewed to the left or right.

1. The process of selecting a sample from a population
2. The list of all elements in the population
3. The margin of error in a confidence interval
4. The probability of making a Type I error

Ans. B

A sampling frame is the list of all elements in the population from which a sample is drawn, serving as the basis for selecting a sample.

1. Central tendency
2. Standard error
3. Variance
4. Mode

Ans. C

Variance is a measure of how much data values are dispersed around the mean in a dataset, indicating the degree of spread.

1. Student’s t-test
2. Chi-squared test
3. Analysis of Variance (ANOVA)
4. Wilcoxon signed-rank test

Ans. D

The Wilcoxon signed-rank test is used to determine if there is a significant difference between the means of two paired groups or conditions when the data is not normally distributed.

1. Skewness
2. Variance
3. Kurtosis
4. Dispersion

Ans. C

Kurtosis is a statistical measure that describes the degree to which data values are concentrated around the mean, indicating the shape of the distribution.

1. Variance
2. Interquartile range
3. Mode
4. Range

Ans. B

The interquartile range is a measure of the spread of data values around the median in a dataset, representing the central 50% of the data.

1. Pearson’s correlation coefficient
2. Spearman’s rank correlation
3. Chi-squared test
4. ANOVA

Ans. B

Spearman’s rank correlation is a statistical measure that describes the strength and direction of a non-linear relationship between two variables by ranking their values.

1. The probability of making a Type I error
2. The likelihood of observing the data or more extreme data, assuming the null hypothesis is true
3. The strength of a linear relationship between two variables
4. The margin of error in a confidence interval

Ans. B

The p-value represents the likelihood of observing the data or more extreme data, assuming the null hypothesis is true, in hypothesis testing. A smaller p-value indicates stronger evidence against the null hypothesis.

1. Type I error
2. Type II error
3. Power
4. Significance level

Ans. C

Power is a measure of the reliability of a statistical test in detecting a true effect, indicating the test’s ability to avoid a Type II error (false negative).

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Binomial distribution

Ans. D

The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, which are experiments with two possible outcomes.

1. R-squared (R^2)
2. Coefficient of determination
3. Pearson’s correlation coefficient
4. Standard error of the estimate

Ans. A

R-squared (R^2) is a measure of the proportion of total variation in a dependent variable explained by independent variables in a regression model.

1. Dispersion
2. Range
3. Skewness
4. Central tendency

Ans. D

Central tendency is the measure of the center of a probability distribution, indicating the typical or central value of a dataset.

1. Analysis of Variance (ANOVA)
2. Chi-squared test
3. T-test
4. Mann-Whitney U test

Ans. C

The T-test is used to compare the means of two independent groups or conditions in a statistical analysis.

1. Regression
2. Correlation
3. Variance
4. Kurtosis

Ans. B

Correlation is a measure of the extent to which two variables change together in a linear relationship, indicating the strength and direction of the relationship.

1. Standard error
2. Interquartile range
3. Mode
4. Skewness

Ans. B

The interquartile range is a measure of how data values tend to cluster around the median in a dataset, representing the middle 50% of the data.

1. Simple random sampling
2. Cluster sampling
3. Stratified sampling
4. Convenience sampling

Ans. A

Simple random sampling is a method in which elements are randomly selected from a population, and every element has an equal chance of being selected, ensuring unbiased representation.

1. Skewness
2. Kurtosis
3. Central tendency
4. Spread

Ans. B

Kurtosis is a statistical measure that describes the shape of a probability distribution, indicating whether it is peaked or flat compared to a normal distribution.

1. Confidence level
2. Z-score
3. Area under the curve
4. Percentile

Ans. C

The term “Area under the curve” represents the proportion of the total area under a normal distribution curve between two specific values, indicating the probability of observing data within that range.

1. Rejecting the null hypothesis when it is true
2. Failing to reject the null hypothesis when it is false
3. The power of the test
4. The probability of making a Type II error

Ans. A

Type I error represents the error of rejecting the null hypothesis when it is true, leading to a false positive conclusion in hypothesis testing.

1. Standard deviation
2. Interquartile range
3. Pearson’s correlation coefficient
4. Mode

Ans. C

Pearson’s correlation coefficient is a measure of the strength of a linear relationship between two variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation), with 0 indicating no linear relationship.

1. The range of data values in a dataset
2. The likelihood of making a Type I error in hypothesis testing
3. The range of values within which a parameter is estimated to fall with a specified level of confidence
4. The margin of error in a confidence interval

Ans. C

A confidence interval represents the range of values within which a parameter is estimated to fall with a specified level of confidence, typically denoted by a confidence level.

1. Student’s t-test
2. Chi-squared test
3. Wilcoxon signed-rank test
4. Analysis of Variance (ANOVA)

Ans. B

The Chi-squared test is used to determine if there is a significant association between two categorical variables, testing the independence of variables in a contingency table.

1. Interquartile range
2. Mode
3. Standard deviation
4. Range

Ans. C

Standard deviation is a measure of the average distance of data values from the mean in a dataset, indicating the degree of dispersion or variability.

1. Range
2. Skewness
3. Interquartile range
4. Mode

Ans. C

The interquartile range is a measure of how data values tend to cluster around the median in a dataset, representing the middle 50% of the data distribution.

1. Chi-squared statistic
2. P-value
3. Pearson’s correlation coefficient
4. Standard error

Ans. C

Pearson’s correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables, providing a value between -1 and 1.

1. The probability of making a Type I error
2. The margin of error in a confidence interval
3. The significance level or threshold for rejecting the null hypothesis
4. The strength of a linear relationship between two variables

Ans. A

The p-value represents the probability of making a Type I error, which is the error of incorrectly rejecting the null hypothesis when it is true.

1. Sensitivity
2. Specificity
3. Precision
4. Accuracy

Ans. A

Sensitivity is a measure that describes the proportion of true positive results out of all actual positive cases in a classification problem, indicating the model’s ability to detect positives correctly.

1. Outlier detection
2. Feature selection
3. Hypothesis testing
4. Imputation

Ans. D

Imputation is a method used to replace missing values in a dataset with estimated values based on other data points, ensuring completeness for analysis.

1. Z-score
2. Confidence level
3. Percentile
4. P-value

Ans. C

The term “Percentile” represents the measure of the proportion of the total area under a probability distribution curve to the left of a specific value, indicating the position of a value within a distribution.

1. Type I error
2. Type II error
3. Power
4. Confidence level

Ans. C

Power is the probability of correctly rejecting the null hypothesis in hypothesis testing, indicating the test’s ability to detect a true effect.

1. Variance
2. Range
3. Standard error
4. Interquartile range

Ans. B

The range is a measure of the spread of data values in a dataset, representing the difference between the maximum and minimum values.

1. Normal distribution
2. Poisson distribution
3. Exponential distribution
4. Binomial distribution

Ans. B

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, given an average rate of occurrence, such as the number of emails received per hour.

1. Median
2. Mode
3. Mean
4. Interquartile range

Ans. C

The mean is the measure of the average value of a set of data points, calculated by summing all values and dividing by the number of data points.

1. The probability of making a Type I error
2. The likelihood that a sample is representative of the population
3. The range of values within which a parameter is estimated to fall
4. The proportion of a population captured by a sample

Ans. A

The significance level in hypothesis testing represents the probability of making a Type I error, typically denoted by alpha (α).

1. Hypothesis testing
2. Confidence interval
3. Regression analysis
4. Bootstrapping

Ans. B

A confidence interval is a method used to estimate population parameters based on sample data, taking into account sampling variability and providing a range of possible values for the parameter.

1. Sensitivity
2. Specificity
3. Precision
4. Accuracy

Ans. B

Specificity is a measure that describes the proportion of true negative results out of all actual negative cases in a classification problem, indicating the model’s ability to correctly identify negatives.

1. R-squared (R^2)
2. Coefficient of determination
3. Pearson’s correlation coefficient
4. Standard error of the estimate

Ans. A

R-squared (R^2) is a measure of the proportion of total variation in a dependent variable explained by independent variables in a regression model, also known as the coefficient of determination.