Part BCSIR NET June 2025r-being-positive-does-not-mean-both-values-actually-occur

R being positive does not mean both values actually occur

Suppose that we have a data set consisting of 2n + 1 observations for some $n \in N$ . Value of each observation is either x or x + r, where $x \in N, r \geq 0$ . Then, which of the following statements is always true?

A.The mean and median of the data will be different if and only if r > 0
B.Variance of the data is positive if and only if r > 0
C.Mean and mode of the data will be same if and only if r = 0
D.Median and mode of the data will be same for all values of r ≥ 0✓

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, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Related counterexample: Uncorrelated ⇒ independent

R being positive does not mean both values actually occur

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