Is the following statement true? Systematic sampling is always at least as efficient as SRS

No. A population with a periodic pattern of period k, sampled every k-th unit Every sampled unit falls at the same phase, so the sample can be maximally unrepresentative.

Counterexample

Is this true?

Systematic sampling is always at least as efficient as SRS

No — it is false.

The counterexample

A population with a periodic pattern of period k, sampled every k-th unit

Why it fails

Every sampled unit falls at the same phase, so the sample can be maximally unrepresentative.

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Keep practicing

Execution slip

The idea was right. The computation was not.

A sufficient statistic is complete
The Cramér–Rao bound is attained by the UMVUE
The MLE is unbiased

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statistics sampling

Go deeper· Explained in full in Sampling designs· Asked in CSIR NET December 2025· From Sampling and Design of Experiments › SRS, stratified and systematic sampling

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.

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