Central Limit Theorem for Quant Interviews
Central limit theorem interview prep for sums, averages, normal approximation, conditions, limits, and common CLT overuse.
Candidates using approximation and statistics intuition in interviews.
The practical intuition
The central limit theorem explains why sums or averages of many small, roughly independent contributions can look approximately normal.
Sums versus averages
Sums grow in scale as more terms are added. Averages stabilize around the mean. Both can be standardized when CLT conditions are reasonable.
Conditions matter
The approximation works best when observations are independent or weakly dependent, no single term dominates, and the sample size is large enough for the setting.
Concrete example
The number of heads in many fair coin flips can be approximated by a normal distribution near the center, with mean np and variance np(1-p).
When not to use it
CLT approximations can be poor in small samples, extreme tails, or distributions dominated by rare huge values. Say when you are approximating.
Common mistakes
Candidates often invoke the CLT as a magic normality rule. Explain what is being summed and why the approximation is plausible.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.