Questions / Quant research, Probability & inference
Uncertainty of an average
Independent observations have known standard deviation 12. With 36 observations, what is the standard error of the sample mean?
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Answer: 2 units
- Independence makes Var(mean) equal to σ²/n. Here that is 144/36 = 4.
- Standard error is the square root of that variance: √4 = 2.
- Equivalently, σ/√n = 12/6. It describes the variability of the sample mean, not of individual observations.
Interview shortcut. Standard error of a mean is σ/√n = 12/6.
Takeaway. Average variances first, then take the square root.
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