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A hydraulic cylinder manufacturing company has decided to outsource the surface hardening process of piston rods to one of the five shortlisted heat treatment companies. Each company has been given 100 piston rods for surface hardening, and any rod with unsatisfactory surface hardness will be rejected. The number of rejected rods is less than 10 for each company. If the median rejection is 5 and the mode is 6, what is the maximum number of piston rods that could be rejected for a single heat treatment company?

Given the mode=6 and median =5 there should be at least two 6 and thus answer should be 6. Is the reasoning correct?

Vikas Sharma
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1 Answers1

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$6$ is the correct answer here, but your

Given the mode=6 and median =5 there should be at least two 6 and thus answer should be 6

may be incomplete. Perhaps better would be something like

If the median of five observations is $5$ then at least half, i.e. three or more companies, had $5$ or fewer rejected rods, leaving two or fewer companies with $6$ or more rejected rods. Since $6$ is the mode, at least two companies had exactly $6$ rejected rods. So here we must have three companies having $5$ or fewer and two companies with exactly $6$. That accounts for all five companies, meaning that the maximum value must be $6$ rejected rods.

Henry
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