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Part CCSIR NET December 2025check-each-statistic-against-the-symmetric-construction-directly-all-four-survive-here

Check each statistic against the symmetric construction directly all four survive here

Consider a dataset of n observations given by A = {x1,x2,…,xnx_{1},x_{2},\dots,x_{n}}. Create a new dataset, given by B = {x1,x2,…,xn,−x1,−x2,…,−xnx_{1},x_{2},\dots,x_{n},-x_{1},-x_{2},\dots,-x_{n}}. Which of the following statements are always true? (Variance is calculated with divisor as the number of observations in the corresponding dataset.)

  1. A.Mean of the observations in dataset B is 0✓
  2. B.Median of the observations in dataset B is 0✓
  3. C.Variance of the observations in dataset B ≥ Variance of the observations in dataset A✓
  4. D.Range of the observations in dataset B ≥ Range of the observations in dataset A✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: Systematic sampling is always at least as efficient as SRS

More on this topic

The chapter behind this: Sampling designs — free to read

From Sampling and Design of Experiments › SRS, stratified and systematic sampling

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