I think the point is being missed here. This response does not answer the direct brief nor the (more important IMHO) underlying question that attempts to excercise empathy for the customer:
"Rank the responses in the order of their relative concern with programming considerations, economic considerations, or other important considerations. If you were the programmer, which approach would you prefer? If you were Mary Jones, which approach would you prefer?"
After 20 years in industry, I constantly see people banging their heads against the wall, not understanding why the customer "doesn't get it," when in many cases they do in fact "get it" but the solution has different meaning to them. The complex challenge is identifying all of their underlying motivations and viewing the problem from their perspective.
Empathizing with the customer is the lesson, not the math. It's important because it makes for a happier professional relationship and if you're technically right, knowing the customer's drivers can help you efficiently negotiate the implementation path forward in a way that everyone is satisfied with and garuntees more future business. The lesson teaches a path to professional happiness, and that's invaluable. Who wants to be grumpy and angry 80% their life?
If someone asks for the median, you supply the median if possible. The assumption underlying the question is that it is difficult to calculate the median.
In fact, in this case, it is not difficult.
Going back to a professional who has requested the median and asking them if they didn't actually want the mean is not a display of empathy. It is patronising. The gender of the stakeholder is perhaps of relevance here.
You certainly shouldn't sneakily make the substitution. However, making a "client" aware of options and the associated trade-offs is very reasonable. Heck, I'd say it's the most professional approach to this problem!
It may be that Mary just needed some measure of central tendency, and would be happier with the mean now versus the median in a week. Alternately, she might need the median specifically for some legally-mandated reporting, and only that will do. You'll never know if you don't ask.
If someone asks for the median, you supply the median if possible
I wouldn't. I have seen first-hand so many projects that took weeks of efforts, because we assume the person making the requirements used perfect language, when they could have been done in a day instead. One word can be the entire difference.
Maybe it happens to you in a big company: "the VP said '...'", so you must do exactly as the VP said. In practice, it turns out that the VP, just like Mary, could easily agree they didn't care if it's median or mean, they just need some number that summarizes the data.
