Tag Archives: Functions

Are you a fair weather fan?

This past weekend my husband and I went first home football game of the season for the Iowa Hawkeyes.  I was excited about the game until I saw the forecast for this past Saturday . . . every day on the news it seemed like the high temperature for the day kept creeping higher and higher.  Finally, on Thursday of last week the air temperature was forecast to reach 94 degrees and the University of Iowa athletic department began posting tips on now to start hydrating now for the game on Saturday.

I called my husband and work and our conversation went something like this:

Me: Did you see the forecast for Saturday?  I think its supposed to be dangerously hot . . .

Husband: Are you trying to bail?

Me: No!  I’m just worried about the heat . . . they said to start hydrating today.

Husband: You’re a fair weather fan!

Really?!? A fair weather fan?

We went.  We had a great time.  The Hawkeyes won.  I didn’t melt.  All in all it was a successful Saturday.

But my experience on Saturday got me thinking about a little thing called the heat index . . . I always thought it of it as the wind chill of really, really hot temperatures.  So, I decided to do a little digging to

  1. Find out about the heat index.
  2. Prove to my husband that I am not a fair weather fan.

According to the National Weather Service, the calculation of the heat index is a regression equation . . .which quite frankly seemed a little complicated for this blog (but if you’d like to see it, look here).

But, I did think that it was interesting that there was an important note when reading the heat index table . . . the NWS warns that the heat index can only be accurately calculated when the humidity and air temperature are represented on the chart.  In other words, this is a domain and range issue.

excessive heat events guidebook cover

There are many situations in mathematics when we’d like to model a particular phenomenon. . .  (heat index, racing times, time-lapse modeling) just to name a few.  And in those situations it does not make sense to have the domain and range be all real number.  Sometimes it doesn’t make sense because the situation represented doesn’t make sense (i.e. negative time) and sometimes it doesn’t make sense because the function will not fit the data as closely if we allow the domain to be all real numbers (as in the case of the racing times).

This past Saturday the temperature at game time was 90 degrees with about 60% humidity . . . we stayed until the end of the third quarter when the Hawkeyes were winning 31-0.  So, what say you . . . am I a fair weather fan?

P.S. If you’re new here, let me let you in on a little secret . . .I love to think about the weather.  Don’t all midwesterners?  Check out a few more weather related posts here and here and here.


Assigning ZIP Codes

Last week I was working on getting a document together that involved typing many, many ZIP codes from across the United States.  This particular document involved looking up addresses for approximately 350 locations and after a while I realized that I was getting pretty darn good at accurately predicting what the first digit of the ZIP code was going to be and vise versa (i.e. if I looked at the first digit of the ZIP code I could guess the location within a few states).

As I was collecting this data into my spreadsheet, I was developing a hypothesis . . . the first digit of the ZIP code is directly related to the year a state joined the union.

Remember, directly related means as the year the state joined the union increases the first digit of the ZIP code also increases.  In other words, the first digit of the ZIP code depends on the year the state joined the union.  To test my hypothesis I used a map of the U.S. and wrote in the first digits of the ZIP codes I knew.

And then, I created a table of values with the same information (X means I didn’t have the ZIP for any location in that particular state, not that a quick Google search couldn’t have helped me find it, but I just didn’t have it in the document I was working from–also, if my hypothesis proved correct I likely wouldn’t need it!):

State ZIP Year of Statehood
Delaware X 1787
Pennsylvania 1 1787
New Jersey 0 1787
Georgia X 1788
Connecticut 0 1788
Massachusetts 0 1788
Maryland 2 1788
South Carolina 2 1788
New Hampshire X 1788
Virginia 2 1788
New York 1 1788
North Carolina 2 1789
Rhode Island X 1790
Vermont 0 1791
Kentucky X 1792
Tennessee 3 1796
Ohio X 1803
Louisiana 7 1812
Indiana X 1816
Mississippi 4 1817
Illinois 6 1818
Alabama 3 1819
Maine 0 1820
Missouri 6 1821
Arkansas 7 1836
Michigan 4 1837
Florida 3 1845
Texas 7 1845
Iowa 5 1846
Wisconsin X 1848
California 9 1850
Minnesota X 1858
Oregon X 1859
Kansas X 1861
West Virginia X 1863
Nevada X 1864
Nebraska X 1867
Colorado X 1876
North Dakota X 1889
South Dakota X 1889
Montana X 1889
Washington X 1889
Idaho X 1890
Wyoming X 1890
Utah X 1896
Oklahoma 7 1907
New Mexico X 1912
Arizona 8 1912
Alaska X 1959
Hawaii X 1959

And I made a scatterplot:


So, I’m going to go ahead and say that my hypothesis was not overwhelmingly correct.  It looks like the year the state joined the union may be related to the first digit of the ZIP code, but clearly my theory has some flaws.  For example, look at the first few entries in the table.  States joining the union after the first few states have ZIP codes of 0, 1, 2!

Ugh.  Then, you know what I wondered about.  Would there have been a need for ZIP codes (i.e. a post office) when the first 13 colonies became states?  In fact, when did the post office start using ZIP codes anyway?  Well, I found my answer . . . 1963.  Yes, really.  1963.

Goodness Gracious.  All 50 states had joined The Union by the time the use of ZIP codes was implemented.

This experience made me think about two things:

1. Just because two variables are correlated, doesn’t mean that one causes the other.

2. I wonder what a better predictor of ZIP codes would be?