Sample Moments (FRM Part 1 2025 – Book 2 – Chapter 5)

Master the sample moments you’ll see on FRM Part 1 – Quantitative Analysis: mean, variance & standard deviation, skewness, kurtosis, quantiles/median, CLT, covariance, correlation, variance-covariance matrix, coskewness, and cokurtosis.
By the end, you’ll be able to:
• distinguish sample vs population moments
• choose unbiased estimators (incl. n–1)
• interpret dispersion, asymmetry, tails, and dependence
• apply CLT logic to sampling questions

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After completing this reading, you should be able to:
Estimate the mean, variance, and standard deviation using sample data.
Explain the difference between a population moment and a sample moment.
Distinguish between an estimator and an estimate.
Describe the bias of an estimator and explain what the bias measures.
Explain what is meant by the statement that the mean estimator is BLUE.
Describe the consistency of an estimator and explain the usefulness of this concept.
Explain how the Law of Large Numbers (LLN) and Central Limit Theorem (CLT) apply to the sample mean.
Estimate and interpret the skewness and kurtosis of a random variable.
Use sample data to estimate quantiles, including the median.
Estimate the mean of two variables and apply the CLT.
Estimate the covariance and correlation between two random variables.
Explain how coskewness and cokurtosis are related to skewness and kurtosis.

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