Statistics MCQs

1. What is the mode of the following data set: 2, 4, 5, 5, 7, 8, 9?
A) 2
B) 5
C) 7
D) 9
Answer: B) 5

2. What does the standard deviation measure in a data set?
A) Central tendency
B) Spread or dispersion
C) Skewness
D) Kurtosis
Answer: B) Spread or dispersion

3. In a boxplot, what does the length of the box represent?
A) Mean
B) Range
C) Interquartile range (IQR)
D) Median
Answer: C) Interquartile range (IQR)

4. What is the formula for calculating the variance of a data set?
A) Sum of squares / Sample size
B) Sum of squares / Degrees of freedom
C) Standard deviation / Mean
D) Mean / Sample size
Answer: A) Sum of squares / Sample size

5. Which of the following measures of central tendency is most affected by outliers?
A) Mean
B) Median
C) Mode
D) Range
Answer: A) Mean

6. What is the range of the data set: 10, 15, 18, 20, 25, 30, 35?
A) 25
B) 30
C) 35
D) 40
Answer: D) 40

7. What is the formula for calculating the coefficient of variation (CV)?
A) Standard deviation / Mean
B) Mean / Standard deviation
C) Range / Standard deviation
D) Mean / Range
Answer: A) Standard deviation / Mean

8. Which measure of central tendency is the middle value in a data set when the values are arranged in ascending order?
A) Mean
B) Median
C) Mode
D) Range
Answer: B) Median

9. What does the term “skewness” refer to in statistics?
A) Measure of spread
B) Measure of symmetry
C) Measure of central tendency
D) Measure of variability
Answer: B) Measure of symmetry

10. In a normal distribution, what percentage of data points fall within one standard deviation from the mean?
A) 25%
B) 50%
C) 68%
D) 95%
Answer: C) 68%

11. What is the formula for calculating the median of a data set?
A) (n + 1) / 2
B) (n – 1) / 2
C) n / 2
D) (n + 2) / 2
Answer: A) (n + 1) / 2

12. Which of the following is a measure of variability in a data set?
A) Mean
B) Mode
C) Standard deviation
D) Median
Answer: C) Standard deviation

13. If the correlation coefficient between two variables is -0.8, what does this indicate?
A) Strong positive correlation
B) Weak negative correlation
C) Strong negative correlation
D) No correlation
Answer: C) Strong negative correlation

14. What is the formula for calculating the interquartile range (IQR)?
A) Q1 – Q3
B) Q3 – Q1
C) Q1 + Q3
D) Q3 + Q1
Answer: B) Q3 – Q1

15. In a boxplot, which part of the plot represents the upper quartile (Q3)?
A) Top whisker
B) Lower edge of the box
C) Middle line of the box
D) Upper edge of the box
Answer: D) Upper edge of the box

16. Which measure of central tendency is affected the least by outliers?
A) Mean
B) Median
C) Mode
D) Range
Answer: B) Median

17. What is the formula for calculating the mean of a data set?
A) Sum of values / Sample size
B) Sum of values / Population size
C) Sum of squares / Sample size
D) Sum of squares / Population size
Answer: A) Sum of values / Sample size

18. What is the purpose of using a scatterplot in statistics?
A) To show the distribution of data
B) To display the relationship between two variables
C) To calculate the mean of a data set
D) To determine the standard deviation
Answer: B) To display the relationship between two variables

19. Which of the following is a measure of the strength and direction of the linear relationship between two variables?
A) Variance
B) Covariance
C) Correlation coefficient
D) Skewness
Answer: C) Correlation coefficient

20. What is the formula for calculating the z-score of a data point in a normal distribution?
A) (X – Mean) / Range
B) (X – Mean) / Standard deviation
C) (X – Mean) / Variance
D) (X – Range) / Standard deviation
Answer: B) (X – Mean) / Standard deviation

21. What does the term “outlier” refer to in statistics?
A) The most frequent value in a data set
B) A data point that lies far from the other data points
C) The median value in a data set
D) The value that appears most frequently
Answer: B) A data point that lies far from the other data points

22. What is the formula for calculating the population variance?
A) Sum of squares / Sample size
B) Sum of squares / Population size
C) Standard deviation / Mean
D) Mean / Sample size
Answer: B) Sum of squares / Population size

23. Which of the following is NOT a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Standard deviation
Answer: D) Standard deviation

24. What is the purpose of using a histogram in statistics?
A) To display the relationship between two variables
B) To show the distribution of categorical data
C) To calculate the mean of a data set
D) To represent the frequency distribution of numerical data
Answer: D) To represent the frequency distribution of numerical data

25. In a normal distribution, what percentage of data points fall within two standard deviations from the mean?
A) 25%
B) 50%
C) 68%
D) 95%
Answer: D) 95%

26. What is the formula for the coefficient of determination (R-squared) in linear regression?
A) Sum of Squares (Regression) / Sum of Squares (Total)
B) Sum of Squares (Error) / Sum of Squares (Regression)
C) Sum of Squares (Total) / Sum of Squares (Regression)
D) Sum of Squares (Total) / Sum of Squares (Error)
Answer: A) Sum of Squares (Regression) / Sum of Squares (Total)

27. Which of the following is a measure of the spread of data around the mean?
A) Variance
B) Median
C) Mode
D) Mean
Answer: A) Variance

28. In statistics, what does the term “population” refer to?
A) A specific group of individuals or objects being studied
B) The entire collection of data or individuals from which a sample is drawn
C) The mean of a data set
D) The median of a data set
Answer: B) The entire collection of data or individuals from which a sample is drawn

29. What is the formula for calculating the sample standard deviation?
A) Sum of Squares / Sample Size
B) Sum of Squares / (Sample Size – 1)
C) Sum of Squares / Population Size
D) Sum of Squares / (Population Size – 1)
Answer: B) Sum of Squares / (Sample Size – 1)

30. What does a p-value in hypothesis testing indicate?
A) The probability of accepting the null hypothesis
B) The probability of rejecting the null hypothesis
C) The level of significance in the alternative hypothesis
D) The level of confidence in the sample mean
Answer: B) The probability of rejecting the null hypothesis

31. Which statistical test is used to compare means of two independent groups?
A) Paired t-test
B) ANOVA
C) Independent t-test
D) Chi-square test
Answer: C) Independent t-test

32. What is the formula for calculating the probability of an event A given event B has occurred (P(A|B))?
A) P(A ∩ B) / P(B)
B) P(A ∪ B) / P(B)
C) P(A) / P(B)
D) P(A) × P(B)
Answer: A) P(A ∩ B) / P(B)

33. What does a correlation coefficient of 0 indicate?
A) No correlation between the variables
B) Perfect positive correlation
C) Perfect negative correlation
D) High variance in the data
Answer: A) No correlation between the variables

34. What does a high p-value in hypothesis testing suggest about the null hypothesis?
A) The null hypothesis is likely to be true
B) The null hypothesis is likely to be false
C) There is strong evidence against the null hypothesis
D) The sample size is too small
Answer: A) The null hypothesis is likely to be true

35. Which of the following is an example of a discrete variable?
A) Height
B) Weight
C) Number of students in a class
D) Temperature
Answer: C) Number of students in a class

36. In a normal distribution, what is the value of the skewness?
A) 0
B) 1
C) -1
D) 0.5
Answer: A) 0

37. What is the formula for calculating the z-score of a data point in a sample?
A) (X – Mean) / Sample standard deviation
B) (X – Mean) / Population standard deviation
C) (X – Sample mean) / Population standard deviation
D) (X – Population mean) / Sample standard deviation
Answer: A) (X – Mean) / Sample standard deviation

38. What does a p-value less than 0.05 typically indicate in hypothesis testing?
A) Strong evidence against the null hypothesis
B) Weak evidence against the null hypothesis
C) The null hypothesis is accepted
D) The sample size is too large
Answer: A) Strong evidence against the null hypothesis

39. In a contingency table, what is the purpose of calculating expected frequencies?
A) To compare observed frequencies with expected frequencies
B) To determine the mode of the data
C) To calculate the mean of the data
D) To estimate the population variance
Answer: A) To compare observed frequencies with expected frequencies

40. Which measure of central tendency is least affected by the presence of extreme values?
A) Mean
B) Median
C) Mode
D) Range
Answer: B) Median

Statistics MCQs

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