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Week 1–4 Statistics Practice Questions
1. Which of the following is a measure of central tendency? A) Variance B) Mean ✅ C) Standard deviation D) Range Correct Answer: B 2. If a dataset has a mean of 50 and a standard deviation of 5, which value is 2 standard deviations above the mean? A) 45 B) 50 C) 55 D) 60 ✅ Correct Answer: D Calculation: 50+2(5)=6050 + 2(5) = 6050+2(5)= 3. A data set contains the values: 2, 4, 4, 4, 5, 5, 7, 9. What is the mode? A) 4 ✅ B) 5 C) 4. D) 5. Correct Answer: A Mode is the most frequently occurring value. 4. What is the probability of rolling a 3 on a fair six-sided die? A) 1/ B) 1/ C) 1/6 ✅ D) 1/ Correct Answer: C 5. A survey finds that 30% of students prefer online classes. What type of probability is this? A) Theoretical
B) Empirical ✅ C) Subjective D) Classical Correct Answer: B Empirical probability is based on observed data.
6. Which graph is best for showing the distribution of a single categorical variable? A) Histogram B) Boxplot C) Bar chart ✅ D) Scatter plot Correct Answer: C 7. If the correlation coefficient r=−0.85r = -0.85r=−0.85, which statement is true? A) There is a strong positive linear relationship. B) There is a weak negative linear relationship. C) There is a strong negative linear relationship ✅ D) The variables are not linearly related. 8. What does the standard deviation measure? A) Central tendency of the data B) Spread or variability of the data ✅ C) Frequency of each value D) Skewness 9. In a normal distribution, approximately what percent of data falls within 1 standard deviation of the mean? A) 50% B) 68% ✅ C) 95% D) 99.7% 10. A sample of 10 students has a mean score of 80. What is the sample mean? A) 10 B) 80 ✅ C) Cannot be determined D) 800
16. The probability of an event A is 0.2. What is the probability of not A? A) 0. B) 0. C) 0.8 ✅ D) Cannot determine 17. If the correlation coefficient r = 0, what does that mean? A) Strong positive relationship B) Strong negative relationship C) No linear relationship ✅ D) Variables are independent 18. Which measure of central tendency is most affected by extreme values? A) Mean ✅ B) Median C) Mode D) Range 19. A probability distribution must satisfy which of the following? A) All probabilities are negative B) Sum of probabilities = 1 ✅ C) Mean = Median D) Standard deviation = 0 20. Which chart is best for showing the relationship between two quantitative variables? A) Histogram B) Scatter plot ✅ C) Bar chart D) Pie chart 21. In a standard normal distribution, the mean is: A) 0 ✅ B) 1 C) 100 D) Depends on the data
22. The interquartile range (IQR) measures: A) Total range of data B) Spread of middle 50% of data ✅ C) Standard deviation D) Mean absolute deviation 23. A researcher randomly selects 5 students from a class of 30. This is an example of: A) Population B) Sample ✅ C) Census D) Experiment 24. A discrete random variable: A) Can take any value within an interval B) Can take only specific values ✅ C) Must be negative D) Has no probability distribution 25. A boxplot shows a dataset with a large upper whisker. This indicates: A) The data is symmetric B) The data is skewed right ✅ C) The data is skewed left D) Mean < Median 26. Which of the following events are mutually exclusive? A) Rolling a 1 and rolling an even number ✅ B) Rolling a 2 and rolling a number less than 6 C) Drawing a red card and a face card D) Rolling a 3 and rolling a number less than 5 27. The complement rule in probability states: A) P(A) + P(not A) = 1 ✅ B) P(A and B) = P(A) × P(B) C) P(A or B) = P(A) + P(B) D) None of the above
C) Mode D) Standard deviation
33. Z-score of a value tells you: A) Its absolute distance from zero B) Its standardized position relative to the mean ✅ C) Probability of the value D) Only used in skewed distributions 34. If a dataset has mean 20 and standard deviation 4, what is the z-score for X = 28? A) 1 B) 2 ✅ C) - D) 8 Calculation: z=X−μσ=28−204=2z = \frac{X - \mu}{\sigma} = \frac{28 - 20}{4} = 2z=σX−μ =428−20= 35. The probability of rolling an even number on a die is: A) 1/ B) 1/2 ✅ C) 1/ D) 2/ 36. The area under the probability density curve equals: A) 0 B) 0. C) 1 ✅ D) Depends on data 37. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent, then P(A and B) = A) 0. B) 0.12 ✅ C) 0. D) 0. Calculation: 0.3 × 0.4 = 0.
38. Which of the following describes a positively skewed distribution? A) Tail is on the left B) Tail is on the right ✅ C) Symmetric D) Bimodal 39. If two events are mutually exclusive, then P(A and B) = A) 0 ✅ B) 1 C) P(A) × P(B) D) P(A) + P(B) 40. A data set has 10 numbers: 5, 7, 8, 12, 13, 14, 15, 18, 20, 22. What is the median? A) 12.5 ✅ B) 13 C) 14 D) 15 Calculation: Middle two values = 12, 13 → Median = (12+13)/2 = 12. 41. The mean of a dataset is 50. One value, 100, is added. What happens to the mean? A) Decreases B) Increases ✅ C) Stays the same D) Cannot tell 42. Which of the following is an example of a continuous random variable? A) Number of heads in 10 coin flips B) Weight of a person ✅ C) Number of students in class D) Number of cars passing a street 43. The interquartile range (IQR) is: A) Difference between max and min B) Difference between Q3 and Q1 ✅ C) Average of Q1 and Q D) Same as standard deviation
50. A probability distribution table shows P(X = x) for all x. What must be true? A) All probabilities are negative B) Probabilities sum to 1 ✅ C) Mean = median D) Only integers are allowed
