Xkcd strip used as a exam question

http://i.imgur.com/fT0DA.png

by adambyrtek • 16 years ago

107 24 16 years ago

i.imgur.com

Maxious• 16 years ago

I've seen this one used in an Introduction to Psychology exam: http://xkcd.com/32/ And the velociraptor problem was a class exercise for calculus: http://www.xkcd.com/135/

tw1st3dst33l2• 16 years ago

This isn't really surprising.I usually find myself wishing that Randall Munroe (author of XKCD) would teach most of my classes. Not only is he a polymath, but he's completely insane. Those are the best teachers.

hugh32• 16 years ago

I'm rather unconvinced that Randall Monroe is a polymath.

xenophanes• 16 years ago

Math and art!! Or do you have a problem with his art!?

wahnfrieden2• 16 years ago

He postures himself as one, at least.

cosmicray• 16 years ago

if they use this one, does it become a recursive loop ? ... nerd sniping: http://xkcd.com/356/

tw1st3dst33l2• 16 years ago

Personally, http://xkcd.com/308/ is what I live my life by.

jtdowney• 16 years ago

We show Exploits of a Mom (http://xkcd.com/327/) with the moms last speech bubble blanked out to candidates during interviews. You might be surprised how many have trouble explaining what is going on.

kenjackson2• 16 years ago

I didn't get it until the last bubble. I thought the son did the exploit and the mom was covering for him. I'm still unclear if that was actually the childs name or this was a one-off exploit by the mom.

wahnfrieden2• 16 years ago

Does that really matter?

The parent poster is saying that interviewees don't get what's going on with the exploit itself.

lgarron• 16 years ago

We had an entire set of programming questions at ProCo (programming contest held at Stanford for high school students) themed with XKCD comics last May: http://cs.stanford.edu/wiki/proco/PastContests/2010Problems

Steuard• 16 years ago

A friend of mine created a nicely organized database of xkcd strips to help teachers find subject-appropriate examples:

http://andromedayelton.com/dckx.php

Some topics clearly show up more often than others...

snes• 16 years ago

Next, everyone will be called a cheater and have to retake the exam because they have read xkcd before.

jawee• 16 years ago

The best I've had in my experience is a Calvin and Hobbes strip, but they're probably too classic to matter.

http://www.gocomics.com/calvinandhobbes/1995/08/23 I had to identify and analyze the survey bias that his response creates for a test in an introductory statistics class.

die_sekte• 16 years ago

Ideal dating pool seems to be around age 32.

I don't know how to optimize a function with an integral in R yet (unsurprising, just installed it 20 minutes ago), therefore I can't give a better answer. Now I want to learn R.

CUViper• 16 years ago

I find it odd that the test's adaptation removes the first two words from "standard creepiness rule: don't date under (age/2+7)". Is it objectionable to refer to dating with large gaps of age as creepy?

waterlesscloud• 16 years ago

Perhaps it's objectionable if you're a professor with a lot of hot students.

kleiba• 16 years ago

I find it creepier when a professor's unwilling to cite a source accurately.

kgroll• 16 years ago

Edit: Just noticed that the Wolfram links break because of their syntax. HN then worsens the problem, by shortening the displayed links with '...', meaning copy/paste breaks! So I'm just removing the http prefix and you'll have to copy/paste to view any of the graphs.

---

This seems to disagree with the gist of the comic, but I think the answer to the final part (largest dating pool) is 23 years old.

I arrived at that by doing the following, please correct me if you spot an error along the way!

The dating range for any age, t, would be defined as:

  lower limit = .5t + 7
  upper limit = 2t - 14

This agrees with the example in the XKCD strip. The dating range for an 18 year old is from .5(18)+7 = 16 to 2(18)-14 = 22. Because this is linear, the range will always be increasing with age.

Despite the range growing with age, we know that the proportion of singles is decreasing with age. Sigh. That's where the other model comes in. The author of this problem gives:

  S(t) = e^(-0.05*t)

That looks like this: www.wolframalpha.com/input/?i=Plot[E^(-0.05+x),+{x,+85,18}]

I believe the largest dating pool would correspond with the greatest area yielded by taking the definite integral of this function from .5t+7 (the lower age limit) to 2t+14 (the upper age limit). To see this in pretty print, you can visit this link: www.wolframalpha.com/input/?i=integrate+(E^(-.05x))+dx+from+(.5x%2B7)+to+(2*x-14)

Evaluating that for any age would give the area under the curve corresponding to that age.

The next step, then, would be to find the maximum area for any age. To do this, we should be able to take the derivative of that previous equation, and set it equal to 0 in order to maximize it. Again, correct me if I'm wrong, but for the result of that, I get:

  -2000(e^(-0.1t+0.7) - e^(-0.025t+0.35)) = 0

I plotted that to find that the max was located at age t = 23.

This graph illustrates the size of the dating pool corresponding to age along the x axis: www.wolframalpha.com/input/?i=Plot[-2000(e^(-0.1x%2B0.7)-e^(-0.025x%2B0.35)),+{x,+0,+100}]

Comments? Did I approach this totally wrong? Did I miss something along the way? Does that seem reasonable?

gmichnikov• 16 years ago

The upper age limit is 2t-14 (as you note earlier in your comment) rather than the 2t+14 you mention later.

Integrating, you get -20(e^(-0.05(2x-14)) - e^(-0.05(x/2+7)))

The derivative (eliminating the constant) is: (e^0.7)(-0.1)(e^(-0.1x))+(e^-0.35)(0.025)(e^(-0.025x))

Wolfram gives about 32.5 as the root. You can plot the integral (try www.coolmath.com/graphit) and mouse over to confirm.

Xkcd strip used as a exam question

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