Monthly Archives: November 2013

M&M’s Revisited (for the Last Time!)

If you haven’t been here before, then you don’t know that we’ve already talked about M&M’s twice (here and here) and you don’t know that we’ve talked a little bit about the colors of M&M’s in the bags.

Well, today I want to keep talking about the different colors of M&M’s in the bags.  Except today I want to talk about the percent of M&M’s that are red, orange, yellow, green, blue, brown.  Before we continue our M&M discussion, do you have a guess?   That is, what percent of the M&M’s manufactured are red, orange, yellow, green, blue, brown?

Hmmm . . . Let’s pretend that we don’t know (maybe you really don’t!).  I think a pretty educated guess would be that 16.67% of the M&M’s are red, 16.67% of them are orange, 16.67% yellow, etc., etc.  Can you live with that guess?

I’m going to use the data I collected in my last M&M post, except instead of individual bags I’m going to look at my entire sample of M&M’s.

Here’s the percentage breakdown of M&M’s:

Screen Shot 2013-11-26 at 9.52.31 AM

Let’s make a nice table, based on what I would expect to get, given my educated guess of 16.67% of each color and what I actually got:

Screen Shot 2013-11-26 at 9.52.41 AM

So, I wonder if the distribution of colors I got in my sample would be likely, if the colors of M&M’s really were distributed evenly at the manufacturer?

Luckily for us there’s a statistical test we can use to answer that exact question.  And, luckily for us its a pretty straightforward test to understand!  It’s called the Chi-Square Goodness of Fit Test.  The Chi-Square Goodness of Fit test compares the observed values (in our case my M&M colors) to the expected values (if our initial assumption was true).  In our case we would subtract the expected value from the observed value and square the difference.  Then, we would divide by the expected value.  We’d do this for each color of M&M and add up the results.  Don’t worry, I’ll do it (actually, I did it with the help of this website). . .

Based on the Chi-Square Goodness of Fit Test it’s fairly reasonable to assume that I could have gotten this distribution of M&M colors given the fact that M&M Mars makes 16.67% of each color of M&M’s.

Screen Shot 2013-11-26 at 10.10.29 AM

So, here’s my next question?  Do they?

(So here’s the thing, about 5 years ago the M&M Mars website used to answer this exact question, but in 2008 they stopped.  This person wrote to M&M’s and posted the response)

Use the distribution for Milk Chocolate M&Ms detailed by M&M Mars and run another Chi Square Goodness of Fit Test with my data (or your own, if you collected any).  How does this compare to the 16.67% guess?

 

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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:

11.19.11

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?

I’m an IOAPA Mentor: Helping Our Students Out of Quicksand

My husband reblogged for the Belin-Blank Center’s blog. Shameless, I know . . . but its just a great post!

belinblank

This is a blog post modified from the blog Be Great! Get Better!.  This post and the post in its original version were written by Matt Degner, principal at South East Junior High School in Iowa City, IA.

I am a sucker for sports movies. My all-time favorite is Major League. I could recite lines from it all day long and laugh to myself. This makes my wife think she married a weirdo, but my brother and friends think it’s pretty cool. The fact that I know Jake Taylor tames Wild Thing, gets the bunt down, reaches first, and helps the Indians win the pennant is enough for me no matter the reaction. During the #IAedchat on October 13, 2013; I found myself thinking how I could relate to the feeling I believe students have when things do not seem to be going well at school.  I…

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For a limited time only . . .

I spent most of last week at the National Association of Gifted Children national conference.  I left Tuesday morning and arrived home Saturday afternoon.  You know how when you’re traveling you kind of loose track of the days of the week?  And, for me, if you’re switching time zones (as I did with this trip) you feel even a little more off kilter?

Well, the day I was getting ready to leave I was scrolling through my Twitter feed and I came across this post from Maths for the Masses:

11.11.12

A wave of panic (briefly) swept through my body!  What in the world is going on?!?!, I thought.  How can it only be September!  I swear I left home on November 6!

(Then, I realized that short dates in the UK are written day/month/year, not month/day/year, as in the US.)

Anyway, the post got me thinking, what are other “once in one hundred-year” dates that we’ll encounter this year?  And how many of these dates will we encounter in the US, but not in the UK and vise versa, based on the different date-writing systems?

Oooo . . . doesn’t this sound fun?  So I started by making a list of fun dates for x/x/13 and the end of the year (12/31/13) to see what I could come up with . . .

There was the obvious 11/12/13 and the aforementioned 9/11/13

How about 7/11/13? (consecutive primes)

or

5/8/13 (consecutive Fibonacci numbers)

then I had to stretch 10/3/13 (10+3=13) or 3/10/13 (same, just the commutative property)

And, in the UK they could have 23/10/13 (you know, 23-10=13) P.S. why won’t people in the US?

What about you?  What are some interesting dates that we’ve come across in 2013? And, did you celebrate?  Personally, I can’t wait until March 14, 2015 at 9:26am.  Do you know why?

On a completely unrelated note, I’m going to start blogging for the Iowa City Mom’s Blog after the first of the year.  If you don’t already, it’d be great if you wanted to check it out!