Saturday, January 31, 2009

I hate the Real World

I am tired of "Real-World" problems.

jd2718 asks about the Integrated Algebra #23
A survey is being conducted to determine which types of television programs people watch. Which survey and location combination would likely contain the most bias?
(1) surveying 10 people who work in a sporting goods store
(2) surveying the first 25 people who enter a grocery store
(3) randomly surveying 50 people during the day in a mall
(4) randomly surveying 75 people during the day in a clothing store

Once again, the real world is far too messy to be contained in a simplistic little problem.  As I said on a different comment, this question was probably written by someone who didn't teach and who didn't completely understand the subject.  In his mind, avoiding bias was only a function of the sample size, but he forgot that this rule applies to those "chosen at random."  

There is simply too little detail to ascertain the randomness of the sample.

The employees at a particular store are probably quite varied and most random, unless you chose all minimum-wage cashiers.  Which is it?

The first 25 people who enter a grocery store would be self-selected as well - none are at work at that time of day,  same type of shopper with same type of viewing habits - they might even have scheduled grocery shopping around their other interests - and may be all getting this chore done so as to go and watch the same show.  Still, 25 grocery shoppers are a better sample than 10 employees if you assume that the 10 are all cashiers.

The 50 in a mall during the day have the same problem - if you have time to go to the mall during the day, you aren't working during the day.  Any mall worker could tell you that - the mornings are the older folks doing their exercise and the idle.  (I am basing this on the advertisements for such at the local mall.  I can't say for sure as I can't recall as I've ever been in the mall during the day on a normal weekday.)  If your survey needed to know daytime viewing habits, this would be the best sample to take, though.

The 75 people during the day in a clothing store are probably the most homogeneous - daytime free time and all that, but the clothing store would select for only a very small demographic.  In my mind, the advantage of the greater number is dwarfed by the uniformity of the clientèle at the Old Navy Store in the mall during the day.

I vote (4) as the most biased sample, based on the assumptions I made. I'm not sure how you can tell me I'm wrong unless I've told you those assumptions.

Once again, real world knowledge, intelligence and critical thinking are a hindrance to the finding "correct" answer, exactly opposite to our goal. 

Oh well.  Shut up, stop thinking and choose (1) as your answer.


  1. I'm sticking with #2. I think the neighborhood/time of day/same food bias probably is more carefully selected than any of the other three.

    I happen to live in a place where different ethnic groups tend to buy their food from different supermarkets. So that does color my view. But, hey, this is New York. This is (pardon me) real.


  2. Yep, forgot about that. Up here in 97% white, northern New England, the Price Chopper and Hannafords are the only two options so everyone goes to one or the other. When I'm in store at basically the same time every week, it does seem as if I know everyone there.

    On the other hand, if during the day I went to the Old Navy in the Mall or the JCPenny's, I can't imagine I'd get much of a cross section of the town - although it IS an amusing thought.

    Damn that real world. We're both right.

    You think they'll change the answer key?