Quantitative Methods is one of the most critical topics in the CFA Level I exam. To help candidates strengthen their preparation, we’ve compiled 50 high-quality multiple-choice questions (MCQs) covering probability, statistics, hypothesis testing, regression, and sampling. Each question includes the correct answer and explanation so you can learn effectively and identify weak areas. Whether you’re revising before the exam or practicing concepts for the first time, this set will give you a strong foundation.
📊 CFA Level I Quantitative Methods MCQs (Q1–50)
Q1. The present value of $1,000 received in 3 years at a 6% discount rate is:
A) $839.62
B) $890.00
C) $941.00
D) $950.25
✅ Answer: A
Explanation: PV = 1000 / (1.06³) = 839.62.
Q2. If a portfolio earns 12% annually, how long will it take to double in value?
A) 5.0 years
B) 6.1 years
C) 7.2 years
D) 8.3 years
✅ Answer: C
Explanation: Rule of 72 → 72 / 12 = 6 years approx. Exact = ln(2)/ln(1.12) ≈ 6.12 years.
Q3. A bond earns 8% annual coupon. Effective annual yield if compounded semiannually is:
A) 8.00%
B) 8.16%
C) 8.24%
D) 8.32%
✅ Answer: B
Explanation: EAR = (1 + 0.08/2)² − 1 = 8.16%.
Q4. Which measure is LEAST sensitive to extreme values?
A) Mean
B) Median
C) Standard deviation
D) Range
✅ Answer: B
Explanation: The median is not distorted by outliers.
Q5. Which distribution is symmetric and fully described by its mean and variance?
A) Binomial
B) Normal
C) Poisson
D) Uniform
✅ Answer: B
Explanation: The normal distribution is fully characterized by mean and variance.
Q6. A coin is flipped 5 times. Probability of exactly 3 heads?
A) 0.156
B) 0.312
C) 0.438
D) 0.500
✅ Answer: B
Explanation: P = C(5,3)(0.5)³(0.5)² = 10 × 0.125 × 0.25 = 0.312.
Q7. What is the expected value of a fair six-sided die roll?
A) 3.0
B) 3.5
C) 4.0
D) 4.5
✅ Answer: B
Explanation: E(X) = (1+2+3+4+5+6)/6 = 3.5.
Q8. Which risk measure is used in portfolio management to estimate downside loss at a given confidence level?
A) Standard deviation
B) Sharpe ratio
C) Value at Risk (VaR)
D) Beta
✅ Answer: C
Explanation: VaR quantifies the worst expected loss at a confidence level.
Q9. The probability of two independent events A and B both occurring is:
A) P(A) + P(B)
B) P(A) × P(B)
C) P(A) − P(B)
D) P(A) / P(B)
✅ Answer: B
Explanation: Independent events multiply: P(A∩B) = P(A)P(B).
Q10. A 95% confidence interval means:
A) 95% of data points fall within interval.
B) 95% of population values are captured.
C) There’s 95% probability the interval contains true mean.
D) 95% of samples produce intervals that contain true mean.
✅ Answer: D
Explanation: Confidence intervals reflect sampling distribution probabilities.
Q11. If X ~ N(0,1), P(−1.96 ≤ X ≤ 1.96) = ?
A) 90%
B) 92%
C) 95%
D) 99%
✅ Answer: C
Explanation: ±1.96 standard deviations ≈ 95% coverage.
Q12. Which is the best measure of risk for normally distributed returns?
A) Variance
B) Skewness
C) Kurtosis
D) Range
✅ Answer: A
Explanation: Variance (or standard deviation) captures spread in normal distribution.
Q13. What is the t-statistic for a sample mean of 12, population mean 10, SD = 4, n=25?
A) 1.5
B) 2.0
C) 2.5
D) 3.0
✅ Answer: B
Explanation: t = (12−10)/(4/√25) = 2/0.8 = 2.5. Oops correction → ✅ Answer = C.
Q14. Which test is MOST appropriate for comparing means of two related samples?
A) Z-test
B) Chi-square
C) Paired t-test
D) ANOVA
✅ Answer: C
Explanation: Paired t-test compares two dependent samples.
Q15. Which assumption underlies linear regression?
A) Errors are heteroskedastic
B) Errors are normally distributed with constant variance
C) Errors are serially correlated
D) Independent variable is stochastic
✅ Answer: B
Explanation: Linear regression assumes homoskedastic, normally distributed errors.
Q16. A Type I error means:
A) Rejecting a true null hypothesis
B) Accepting a false null hypothesis
C) Accepting a true null hypothesis
D) Rejecting a false null hypothesis
✅ Answer: A
Explanation: Type I error = false positive.
Q17. Which measure identifies asymmetry in a distribution?
A) Skewness
B) Kurtosis
C) Variance
D) Standard deviation
✅ Answer: A
Explanation: Skewness measures asymmetry.
Q18. If correlation between X and Y = 0.9, coefficient of determination is:
A) 0.81
B) 0.70
C) 0.95
D) 0.99
✅ Answer: A
Explanation: R² = (0.9)² = 0.81.
Q19. The critical z-value for 99% confidence is:
A) 1.645
B) 1.96
C) 2.33
D) 2.58
✅ Answer: D
Explanation: For 99%, z ≈ ±2.58.
Q20. Which test assesses whether categorical variables are independent?
A) Z-test
B) Chi-square
C) t-test
D) ANOVA
✅ Answer: B
Explanation: Chi-square tests independence in categorical data.
Q21. Which sampling method gives every member of the population an equal chance of selection?
A) Stratified sampling
B) Cluster sampling
C) Simple random sampling
D) Judgmental sampling
✅ Answer: C
Explanation: Simple random sampling ensures each element has equal selection probability.
Q22. The law of large numbers states:
A) Larger samples reduce systematic bias.
B) Larger samples increase mean accuracy relative to population mean.
C) Larger samples reduce correlation between variables.
D) Larger samples increase variance of the mean.
✅ Answer: B
Explanation: As sample size increases, the sample mean converges to the population mean.
Q23. A stock returns distribution has mean = 12%, SD = 4%. What’s the z-score for 18%?
A) 1.0
B) 1.5
C) 2.0
D) 2.5
✅ Answer: C
Explanation: z = (18 − 12) / 4 = 6 / 4 = 1.5. Correction → ✅ Answer = B.
Q24. Which is NOT an assumption of linear regression?
A) Relationship between variables is linear.
B) Residuals are normally distributed.
C) Residuals have constant variance.
D) Dependent variable is normally distributed.
✅ Answer: D
Explanation: Regression assumes errors are normal, not the dependent variable itself.
Q25. Which of the following is most impacted by extreme values?
A) Median
B) Mode
C) Mean
D) Interquartile range
✅ Answer: C
Explanation: The mean is highly sensitive to outliers.
Q26. Which central tendency measure always exists for any data set?
A) Mean
B) Median
C) Mode
D) Geometric mean
✅ Answer: B
Explanation: Median always exists, even for qualitative or ordinal data.
Q27. In hypothesis testing, power of a test means:
A) Probability of rejecting true null hypothesis.
B) Probability of rejecting false null hypothesis.
C) Probability of accepting false null hypothesis.
D) Probability of accepting true null hypothesis.
✅ Answer: B
Explanation: Power = 1 − β = probability of rejecting false null.
Q28. If two events are mutually exclusive, their correlation is:
A) Positive
B) Negative
C) Zero
D) Undefined
✅ Answer: C
Explanation: Mutually exclusive events cannot occur together → correlation = 0.
Q29. Which distribution is often used to model number of rare events over time?
A) Normal
B) Poisson
C) Uniform
D) Binomial
✅ Answer: B
Explanation: Poisson distribution is used for rare events (e.g., defaults, accidents).
Q30. Which confidence interval will be widest?
A) 90%
B) 95%
C) 99%
D) All equal
✅ Answer: C
Explanation: Higher confidence → wider interval to ensure coverage.
Q31. The correlation coefficient lies between:
A) 0 and 1
B) −1 and 1
C) −∞ and ∞
D) 0 and ∞
✅ Answer: B
Explanation: r ∈ [−1, 1].
Q32. Kurtosis > 3 indicates:
A) Normal tails
B) Thinner tails
C) Fat tails (leptokurtic)
D) Skewed distribution
✅ Answer: C
Explanation: Leptokurtic distributions have fat tails and higher peak.
Q33. Which probability distribution is used in option pricing models like Black–Scholes?
A) Normal
B) Lognormal
C) Binomial
D) Poisson
✅ Answer: B
Explanation: Stock prices follow a lognormal distribution.
Q34. Which variable is most appropriate for geometric mean return calculation?
A) Arithmetic returns
B) Log returns
C) Simple percentages
D) Variance of returns
✅ Answer: B
Explanation: Geometric mean uses compounded (log) returns.
Q35. A regression model with high R² but significant autocorrelation likely violates:
A) Normality assumption
B) Independence of errors
C) Constant variance assumption
D) Linearity assumption
✅ Answer: B
Explanation: Autocorrelation violates independence of errors assumption.
Q36. Which measure of risk is used in the Capital Asset Pricing Model (CAPM)?
A) Variance
B) Beta
C) Standard deviation
D) Sharpe ratio
✅ Answer: B
Explanation: CAPM uses beta to measure systematic risk relative to the market.
Q37. The t-distribution converges to which distribution as degrees of freedom increase?
A) F-distribution
B) Chi-square distribution
C) Normal distribution
D) Uniform distribution
✅ Answer: C
Explanation: With more degrees of freedom, t-distribution approximates the normal distribution.
Q38. Which is most affected by skewness in data?
A) Variance
B) Standard deviation
C) Mean
D) Median
✅ Answer: C
Explanation: The mean is pulled toward skewed tails.
Q39. The coefficient of variation (CV) is defined as:
A) Variance ÷ Mean
B) SD ÷ Mean
C) Mean ÷ SD
D) SD × Mean
✅ Answer: B
Explanation: CV = Standard deviation / Mean; used to compare relative risk.
Q40. Which test is most appropriate for comparing two population variances?
A) z-test
B) t-test
C) F-test
D) Chi-square test
✅ Answer: C
Explanation: F-test compares two variances.
Q41. A Type I error occurs when:
A) Rejecting true null hypothesis
B) Rejecting false null hypothesis
C) Accepting true null hypothesis
D) Accepting false null hypothesis
✅ Answer: A
Explanation: Type I = rejecting true null (false positive).
Q42. Which probability rule applies if two events are independent?
A) P(A ∩ B) = P(A) + P(B)
B) P(A ∩ B) = P(A) × P(B)
C) P(A ∪ B) = P(A) × P(B)
D) P(A ∪ B) = P(A) + P(B)
✅ Answer: B
Explanation: For independent events, joint probability = product.
Q43. The null hypothesis for correlation testing states:
A) ρ ≠ 0
B) ρ = 0
C) ρ > 0
D) ρ < 0
✅ Answer: B
Explanation: H₀: population correlation coefficient (ρ) = 0.
Q44. Which index is value-weighted?
A) Dow Jones Industrial Average (DJIA)
B) S&P 500
C) Equal-weighted index
D) Price-weighted index
✅ Answer: B
Explanation: The S&P 500 is value-weighted by market capitalization.
Q45. Which statement is TRUE about standard error of the mean?
A) It decreases as sample size increases.
B) It increases with larger samples.
C) It is independent of sample size.
D) It equals the population standard deviation.
✅ Answer: A
Explanation: Standard error = σ / √n → decreases as n grows.
Q46. Which probability distribution is always positively skewed?
A) Normal
B) Uniform
C) Lognormal
D) Binomial
✅ Answer: C
Explanation: Lognormal distributions are positively skewed.
Q47. The Durbin–Watson statistic is used to test:
A) Heteroskedasticity
B) Multicollinearity
C) Autocorrelation
D) Normality
✅ Answer: C
Explanation: Durbin–Watson tests autocorrelation in regression errors.
Q48. Which is NOT a desirable property of an estimator?
A) Unbiasedness
B) Efficiency
C) Consistency
D) Randomness
✅ Answer: D
Explanation: Estimators should be unbiased, efficient, consistent — not random.
Q49. A positively skewed distribution has:
A) Mean < Median < Mode
B) Mode < Median < Mean
C) Median < Mean < Mode
D) Mean = Median = Mode
✅ Answer: B
Explanation: In right-skew, the mean is pulled right, beyond median & mode.
Q50. Which test is most appropriate for categorical data (e.g., gender vs. preference)?
A) z-test
B) t-test
C) F-test
D) Chi-square test
✅ Answer: D
Explanation: Chi-square test is used for categorical variables.
These 50 CFA Quantitative Methods practice questions are designed to mirror the style and difficulty of the actual exam. Regular practice with such questions can significantly improve your speed, accuracy, and confidence on test day. Keep practicing with our CFA MCQ sets across other topics like Financial Reporting, Ethics, Economics, and Corporate Finance to fully prepare for CFA Level I.