# 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:

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:

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.

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?

# 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?

# 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!

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:

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!