Six shifted numbers have median 8. Find their mean.

01 / Standard#Your turn

x+2,x+3,x+4,x-4,x-5,x-6

Official paper · jm01-2025 · I.8 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Sort the six expressions by their offsets.

Hint 2

The median is the average of the third and fourth sorted values.

Worked solution

C: 8.

Checks and common pitfalls: The unsorted third and fourth entries do not define the median.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The middle two values are x−4 and x+2.
$\frac{(x-4)+(x+2)}2=x-1=8\implies x=9$
The sum of all six offsets is −6.
$\bar x=\frac{6x-6}6=x-1=8$

Think first. Reveal a hint when the class is ready.

2025 JM01