Maximum total score 36.5

Class median 32


1. Close encounters

(a) (2 points) "Prox" is short for proximity.  How close is that?
Measure the distance from the sensor at which your prox card unlocks the
door.  Do the experiment 5 times under constant conditions and report
all 5 distances.  Be careful, but don't fudge: there's no reason to
expect that the result will be the same each time, and one of the
purposes of the experiment is to see how variable the sensitivity is.

  There should be five numbers; it doesn't matter what they are,
  except that they shouldn't have more than about 2 significant
  figures for the distances. 

  -1 for just single number

(b) (2 points) Normally the prox works even if it's in a pocket or a
purse.  Find a (non-destructive!)  way to prevent the sensor from
noticing your card even if you hold it quite close.

  I was looking for something like wrapping it in some metallic
  shield, but anything else that seems remotely sensible is fine.

  -1 if it is destructive

(c) (3 points) Distance sensitivity is only one of a variety of
experiments that one might perform to determine properties of the prox
card system.  Describe three similarly simple and plausible experiments
that you could perform that would not arouse the interest of Public
Safety and that would not damage your card.  A single clear phrase or
sentence that states what you would be trying to determine and what you
would do is enough for each.  For example, "Test whether the sensitivity
varies during the day by measuring the distance at 4-hour intervals."
You don't have to actually perform the experiments, though you're
welcome to do so.

  Anything sensible, like angle of approach, wrapping material,
  etc., but don't give credit for things that are really exactly
  the same, like "measure the effect of holding it horizontal,
  measure the effect of holding it vertical".

  1 for each experiment.  -0.5 if one experiment is almost same as
  another (e.g.  test whether sensitivity varies due to aluminum
  obstruction, test whether sensitivity varies due to rubbber
  obstruction) No point if the experiment is not about properties
  of the prox card, but about the policy of the university.  No
  point if the experiment damages the card.
             

(d) (3.5 point) Your prox has a number of visible things that identify
you specifically.  List them all.

  picture
  ID number
  name
  bar code
  bar code number
  mag strip
  another number at the bottom of the card. 

  no credit for answers like "Student" or birthday
  or dorm name that don't identify a person specifically.

  0.5 for each of the right answers. -0.5 for each of the wrong answers.
  This means that each wrong answer cancels a right answer.

(e) (2 points) You open doors by waving the prox, you get food by
swiping it, and the library uses yet another mechanism when you check
out a book.  Suggest a plausible explanation for why the library neither
waves nor swipes.

  my guess: all library books already have a bar code so it's just
  easier to scan the student's card and the books with the same
  device at the same time.  anything else would require two boxes
  on the counter and would cost twice as much.  also, putting a
  bar code in a book has got to be simpler than any of the
  alternatives.  give reasonable credit for something sensible,
  but it should be at least plausible.

  -1 if there is no explanation for 'why'

2. Estimation

(a) (3 points) How many times a week (total for all undergrads) are prox
cards used to enter dorms?

  I'm looking for something like "I use mine 5 times a day, and
  there are 5000 students, so 25000 a day, or 175000 a week".  I
  have no idea what the busy hour is, though it's probably lunch
  or dinner.  Anything goes here, but they should correctly
  compute the ratio for their values.

  Again not too many significant figures in any of these: there is
  no such thing as a right answer so they should not provide more
  than round numbers like 175000 or 180000 or the like.

  Full credit if the answer considers only one class, or answers
  for all prox card uses (including swipe for meal plan, etc.)
  -1 for the answers calculating times a day, not times a week.

(b) (i) (2 points) How many bytes might it take to store a record of a
typical single transaction: a particular student opens a specific
entry/door at a specific time on a specific date?  (Think of the number
of characters you would have to write down if you were doing this by
hand; each of those is at most one byte on a computer.)

Write down what might be in one such transaction, just to make your
numeric answer concrete.

  Maybe 15-20 bytes for a name, 10-20 for a date and time, 5-20
  for the entry?  Doesn't much matter, though it should be in the
  general range of maybe 30-60.

  They have to write down an example and it ought to be at least
  somewhat consistent with what they estimate.

  -1 if any of the entries are missing.

  -1 for the wrong assumptions (e.g.  1 bit can represent 1
  character.  1 byte is enough for student name or student ID).

  No score if there is no justification about the answer.

(ii) (1 points) Roughly how many megabytes would be required to hold the
records for all students for one week?

  They just have to multiply their answer to (a) by their answer to (b).

(c) (2 points) If you had records for a bunch of transactions, say an
entire semester, you might be able to compress the information so it
takes less space.  Briefly describe a way that you might be able to do
this compression.  We're not looking for anything sophisticated here,
just an idea that might work.  It may help to think about what's
repetitive and thus redundant and thus only needs to be stored once for
a large group of related transactions.

  Full marks if they realize that they could group all the records
  that share something, like building or date or name, and then
  have only one instance of the shared information.

  -1 if the compression method proposed causes the loss of
  information (e.g.  instead of logging every transactions, log
  transactions for every five minutes).
  -1 if the answer is not specific enough. 

(d) (2 points) Suppose a surveillance system takes a picture of each
student each time they use their prox.  How many gigabytes (very
roughly) would be required to store these pictures over the course of
one academic year?  Be as quantitative as necessary to support your
position, but not excessively so -- this is a question about ballpark
figures.  The "right" answer here will depend on your assumptions, so
state them clearly.

  I think some have never looked to see how big an image file is.
  But they should just multiply that size (around 1-2 MB/picture?)
  by the number of entries during a week (200,000?) times the
  number of weeks (30?), so 5-10 TB?  Anything vaguely sensible is
  fine.


3. Fuzzy Math and Flaky Numbers

These problems ask you to assess some numbers and arithmetic from other
people.

(a) (2 points) An advertisement for Excelsior College in the New York
Times on 9/14/10 said "According to 2008 Census data, the median
earnings of someone with a bachelor's degree was $47,853, or 43 percent
higher than the $27,448 earned by someone with only a high school
diploma."  Assuming that the dollar figures are correct, what's the
correct percentage?

  47853/27448 = 1.743, so about 74%
 
  -1 for 27448/47853 = 57%

(b) A story in the Toronto Globe and Mail on 8/24/11 said "Canadians
spent 61,267 minutes online in June, a 7 percent increase from the year
before, according to Internet tracking firm Comscore.  A major slice of
that time, 25,587 minutes total, was spent watching video -- a 42
percent increase from last year."

(i) (2 points) What were the corresponding numbers for the previous
year?

  61267 / 1.07 = 57259
  25587 / 1.42 = 18019
	They have to provide both numbers.

  -0.5 for the answer mutiplies 0.93(0.58) instead of divide by 1.07(1.42).

(ii) (1 points) Are the time values reasonable?  Specifically, is 61,267
minutes likely to be much too high, much too low, or about right, and
why do you say so?

	Much too low: it's 61000/34000000 or 0.0018 minutes/month.
	They have to give some quantitative reasoning; saying it's
	ridiculous gets no credit, nor does saying "There's no way
	to answer the question."

(iii) (2 points) From your own experience, how much time do you think a
typical person might spend online in a month?  From that, how much time
will Canadians spend online in a month?  (There are about 34 million of
us.)

  Any sensible number, like 2 hours/day = 60 hours/month,
  then correctly multiplying by 34M, and not too many significant figures.

(c) A story on Slashdot on 6/28/10 says that "Facebook's 400 million
users spend more than 16 billion minutes on the site every day, and view
1 million photos every second."

(i) (2 points) On average, approximately how long does each user spend
looking at a single picture?

  If you assume that Facebook people do nothing but look at
  pictures, then you can compute a value this way.  Users use FB
  16 billion minutes per day, so with 400 M users, that's 40
  minutes per user per day.  There are 1 million picture views per
  second, so 2400 million views in 40 minutes total, so 2400/400 =
  6 views per user, so 40/6 minutes each.

  If people have a different but vaguely sensible interpretation,
  that's ok too as long as they do correct arithmetic.

  -0.5 if there are some formulars but no final answer.
  -0.5 for misinterpretation of the question.
   -1 if there is no justification about the answer. 

	Since the wording of the question was unclear, gives 1 point as
	default for every submissions.

(ii) (1 point) Facebook currently claims over 750 million users.  What
percentage growth is that since 6/10?

  750/400 = 87.5%

  -0.5 for 400/750.

(d) According to a New York Times story on 9/9/11, Google servers use
260 megawatts worldwide, and people do over a billion searches a day,
presumably also a worldwide number.  The story goes on to say that the
average energy for a typical user is about 180 watt-hours a month, and
an average search uses 0.3 watt-hours.  (A watt is a measure of
instantaneous power consumption; a watt-hour is consumption of one watt
for one hour, or two watts for half an hour, etc.)

(i) (1 point) If a Google user only does searches, how many searches per
month per user does this power use correspond to?

  180/0.3 = 600

(ii) (3 points) If these numbers are correct, what fraction of Google's
total energy consumption is caused by searches?

  total search energy = 10^9 * 0.3 = 300 * 10^6 watt-hours / day
  Google energy use = 260 * 10^6 * 24 = 6240 * 10^6 watt-hours / day
  fraction = 300/6240 = 4.8%

  1 point for each of steps above