Question

Brianna asks 7 classmates how many pens and pencils they carry in their bags. The mean number of pens is 10. The mean number of pencils is 6. The mean absolute deviation​ (MAD) of both data sets is 2. What inference could Brianna make using this​ data?
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Part 1
Choose the correct answer below.
A.
Most of​ Brianna's classmates carry more pencils than pens in their bags.
B.
Most of​ Brianna's classmates carry more pens than pencils in their bags.
C.
All of​ Brianna's classmates carry at least 10 pens in their bags.
D.
Most of​ Brianna's classmates carry similar amounts of pens and pencils in their bags.

Answer 1

B. Most of Brianna's classmates carry more pens than pencils in their bags.

Reason: The mean number of pens is 10 and the mean number of pencils is 6 (a difference of 4). The MAD of 2 for each set means most pen counts are about 2 away from 10 (roughly 8–12) and most pencil counts are about 2 away from 6 (roughly 4–8). Those ranges place typical pen counts above typical pencil counts, so most classmates likely carry more pens than pencils.