CFA Level I Quantitative Methods Practice Questions

Correct answer: D. 84%

Chebyshev's inequality holds for any distribution and states that at least 1 - 1/k^2 of observations fall within k standard deviations of the mean. With k = 2.5, the bound is 1 - 1/6.25 = 0.84, or 84%.

• AA. This is 1 - 1/k with k = 2.5, which uses the wrong formula and omits the square.
• BB. This is the Chebyshev bound for k = 2, not 2.5.
• CC. This is the approximate share within two standard deviations of a normal distribution, which cannot be assumed here.
• DD. Correct: 1 - 1/(2.5)^2 = 84%.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: D. The mean will typically be higher than the median, because the extreme high values pull the mean upward

In a right-skewed distribution, extreme values in the long right tail pull the arithmetic mean upward more than they affect the median. The typical ordering is mode < median < mean for right-skewed data.

• AA. Incorrect. The mode doesn't work this way; in a typical right-skewed unimodal distribution the ordering is mode < median < mean, not mode above both.
• BB. Incorrect. This states the opposite relationship; in a right-skewed distribution the mean typically exceeds the median, not the reverse.
• CC. Incorrect. Mean and median are only exactly equal in a symmetric distribution; skew by definition creates a gap between them.
• DD. Correct. In a right-skewed (positively skewed) distribution, a few extreme high values pull the mean above the median.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: B. 3.16

Mean = 8. Squared deviations sum to 40. Sample variance = 40/(n−1) = 40/4 = 10, so sample standard deviation = √10 ≈ 3.16. Choice A mistakenly divides by n (population convention). Choice C reports the variance, not std dev.

• AA. 2.83 equals the square root of 8, which results from dividing the sum of squared deviations by n (the population convention) instead of n-1, then taking the square root.
• BB. Mean = 8; squared deviations sum to 40; sample variance = 40/(5-1) = 10; sample standard deviation = square root of 10, approximately 3.16.
• CC. 8.00 is the population variance (40/5), not a standard deviation. The square root step was never taken.
• DD. 10.00 is the correct sample variance itself (40/4), but the square root step needed to convert variance into standard deviation was omitted.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: C. The null hypothesis is true, but the test incorrectly rejects it.

A Type I error is the rejection of a true null hypothesis. A 'false positive.' Its probability is the test's significance level, α. A Type II error, by contrast, is the failure to reject a false null hypothesis. A 'false negative,' whose probability is denoted β.

• AA. Incorrect. This describes a correct decision (true null, correctly not rejected) at the 5% level, not an error.
• BB. Incorrect. This describes a correct decision (false null, correctly rejected), related to the test's power, not an error.
• CC. Correct. Rejecting a true null hypothesis is precisely the definition of a Type I error, with probability α.
• DD. Incorrect. This describes a Type II error, not a Type I error.

• Source: CFA Institute refresher reading: Hypothesis Testing, accessed October 2026

Correct answer: C. Student's t-distribution with 19 degrees of freedom

When the population variance is unknown and the sample is small, the t-distribution with n − 1 degrees of freedom is the appropriate basis for the reliability factor. With n = 20, degrees of freedom = 19.

• AA. Incorrect. This uses the correct distribution but the wrong degrees of freedom (should be n − 1, not n).
• BB. Incorrect. The z-distribution is appropriate when the population variance is known or the sample size is very large, neither of which applies here.
• CC. Correct. Unknown population variance calls for the t-distribution, and degrees of freedom equal n − 1 = 19.
• DD. Incorrect. The chi-square distribution is used for tests concerning a population variance, not for confidence intervals around a mean.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: B. $16,561

This is an ordinary annuity. PV = PMT × [1 − (1+r)^−n] / r = 5,000 × [1 − 1.08^−4] / 0.08 = 5,000 × 3.31213 = $16,561 (rounded). Choice A ignores time value of money entirely. Choice C mistakenly treats the cash flows as an annuity due, and D mistakenly uses n=5.

• AA. Incorrect. $20,000 is simply 4 × $5,000 with no discounting at all; it ignores the time value of money implied by the 8% rate.
• BB. Correct. PV = $5,000 × [1−(1.08)^−4]/0.08 ≈ $5,000 × 3.3121 ≈ $16,561.
• CC. Incorrect. $17,885 doesn't match the ordinary annuity formula at 8% for 4 years; recheck whether payments were mistakenly treated as occurring at the start of each year (annuity due) instead of the end.
• DD. Incorrect. $19,964 is too close to the undiscounted total and doesn't reflect proper discounting of all four cash flows at 8%.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: B. $13,382

FV = PV(1+r)^n = 10,000 × (1.06)^5 = 10,000 × 1.338226 = $13,382 (rounded). Choice A results from mistakenly applying simple interest. Choice C uses n=4 instead of 5, and Choice D uses n=6 instead of 5.

• AA. Incorrect. $13,000 reflects simple interest ($10,000 × 6% × 5 years added on top), not annual compounding.
• BB. Correct. FV = $10,000 × 1.06^5 = $13,382.
• CC. Incorrect. $12,625 corresponds to compounding over only 4 years (1.06^4), one period short of the required 5.
• DD. Incorrect. $14,185 corresponds to compounding over 6 years (1.06^6), one period too many.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026

Correct answer: C. 6.17%

EAR = (1 + periodic rate)^m − 1 = (1 + 0.06/12)^12 − 1 ≈ 1.0617 − 1 = 6.17%. Monthly compounding produces an EAR above the stated annual rate because interest earned within the year itself earns additional interest.

• AA. Wrong. This is just the stated nominal annual rate, ignoring the effect of intra-year compounding.
• BB. Wrong. Resembles a value from assuming an incorrect (e.g., quarterly) compounding frequency.
• CC. Correct.
• DD. Wrong. Overstates the compounding effect, consistent with assuming a higher compounding frequency than monthly.

• Source: Exam outline: CFA Institute 2026 Level I Topic Outlines (learning outcomes), accessed October 2026