PEA 2026 PEA Q14 | ISI MSQE

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2026 PEA Q14

A dataset consists of $9$ observations arranged in increasing order $x_1 \le x_2 \le \cdots \le x_9$ with mean $20$ and median $18$ . If $x_9$ is replaced by a very large number, which must be true?

Reveal answer and solution

Answer

Solution

1
The median of $9$ ordered observations is $x_5$ , which is unaffected by changing
2
the largest observation $x_9$ (the ordering is preserved). The mean equals the
3
sum divided by $9$ , so increasing $x_9$ raises the sum and hence the mean.

Answer structure / marking notes

The median is robust to extreme values; the mean is not.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2026/ISI_MSQE_PEA_2026_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.