core practice · coding problem
Standard error vs standard deviation
n=100 samples, sample mean x̄=50, sample SD s=10. Compute SE = s/√n and a 95% CI for the population mean (use z=1.96). Why is SE smaller than s?
The mechanism
Your data is one draw from a bigger game. The CLT says sample means from many independent pieces look Normal even when the underlying data is not — which is why confidence intervals and z-tests work on proportions and averages.
Expected evidence
SE=10/10=1; CI≈[48.04, 51.96]. SE describes uncertainty of the mean; s describes spread of individual points.
Try this drill in the practice workspace →
Hints when you need them
- SE = s/√n.
- CI = x̄ ± z·SE.
Watch for these mistakes
- Applying CLT with n=5 and calling it rigorous
- Treating the sample as the population
- Ignoring dependence across samples (e.g. time-series)