Tag Archives: Statistics

10,000 step challenge

This year I asked for a FitBit for my birthday.  (For those of you that don’t know a FitBit is a pedometer, counting your steps, flights of stairs, daily active minutes, and approximate number of calories burned).  I was excited and curious to clip on my FitBit and see just how far I was walking every day!

But, after a few, short days I was a little confused.  I thought that about 2,000 walking steps = 1 mile, but I was getting FitBit read-outs on my phone that looked like this:

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So, if you’ve been reading this blog for any amount of time, you can probably guess what I did next . . .Yep, I Googled the length of a walking step and discovered that this website (which seems legit to me) estimates that the average length of a person’s walking step is about 2.5 ft, which means that in order for a person with average walking steps to walk 5 miles, they’d have to take 10,560 steps . . . not 10,000.

Then, I started wondering how long my steps were (on average of course); compared to the published average of 2.5 feet/step.  I used my FitBit output for 3 different days

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and discovered that, despite my relatively short legs my walking stride length was pretty average!

Then, I started thinking about a project I used to have some of my students work one, which is now an activity on the NCTM Illuminations Site, called Walking to Class.

This summer, make a walking strides chart of your day (or a trip to and from the park, pool, etc.) but instead of measuring distance in steps, change the units from steps to miles using the average 2.5 foot length, or you could dust off a pedometer and calculate the length of your actual stride!

 

In like a Lion; Out like a Lamb?

This morning as I was walking to work through whipping wind and freezing cold temps, I thought to myself “March, you’re supposed to be going out like a lamb.”  Goodness knows it sure came in like a lion!  Then, I started thinking about Groundhog’s Day and how unreliable that good old Phil actually is!  That made me wonder . . . is there really any truth to this whole lion/lamb thing?

I spent the better part of my morning trying to track down an answer!

This is what I did:

I’m only concerned with how March comes in and out, and not what happens in the middle of the month, so I thought I’d look at the first 7 days of March and the last 7 days of March.  Then, I did a quick search and found that the average March temperature in Iowa for the past 150 years is 34.5 degrees Fahrenheit.

Given this information I decided I would define “Lion” to be a 7-day span in which 4 or more of the days had an average temperature that was less than the average monthly temperature.  Then, a “Lamb” was a 7-day span in which 4 or more of the days had an average temperature that was greater than or equal to the average monthly temperature.

I obtained daily average temperature data for Des Moines from The University of Dayton Average Daily Temperature Archive dating back to 1995.  Because the month of March isn’t over yet for 2014, I didn’t use the temperature data for any of the days in March 2014.  This is what I came up with:

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In the past 19 years March has followed the “In like a Lion; Out like a Lamb,” pattern in 13 different years (or 68% of the time).  It has followed an “In like a Lamb; Out like a Lamb” pattern 5 different years (or 26% of the time).  And once in the last 19 years March has come in like a Lion and gone out like a Lion . . . according to the average daily temperature in Des Moines.

This got me thinking about a few things:

1. This saying seems to be a little more accurate then the Groundhog shadow thing.

2. There weren’t any “In like a Lamb; Out like a Lion” years . . . I wonder how many times that has happened in the past 150 years (if at all)?

3. What do you think of my definition for Lion-like weather and Lamb-like weather?  Would you define it another way?  If so, how?

Math Dice Game

My mom bought me this little game called “Math Dice” for Christmas this year.  Have you heard of it?  I hadn’t, and truth be told, I’m not sure my mom realized it was a game she was buying it for me.

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When I opened the package she said “I thought you could do something creative with those dice and your math blog.”  In the days after Christmas, I scooped the unopened box of dice into our “junk drawer” (sorry mom) and rediscovered them this weekend while cleaning.  On the back the of the box were the directions to the “Math Dice Game.”

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This morning I had a little extra time, so I thought I’d give the game try!

Step One: Roll the 12-sided target dice

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Step Two: Roll the three 6-sided scoring dice.  Combine the three scoring dice in anyway to match or come closest to the Target Number.

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Ummm, really?  1, 1, 2?  The closest I could get to 80 was 24.  This is what I did:

(1+1+2)! = 4*3*2*1.  Can you get closer?

My second roll of the Target Dice was 36

My Scoring Dice roll was 6, 4, 2

Super easy: (6*(4+2))=36.  Did you get 36 another way?

My last roll was 20

And my scoring dice were 6, 3, 1

I couldn’t get 20.  I could get 18 and 21, but 20 right on the money was a little tricky.  Can you do it?

Much, much more to come about this fun Math Game, with my new Math Dice . . . I’m working on a table of possible Target Number combinations as we speak!

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:

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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:

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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.

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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?

 

TIme Lapse Photography

This week’s math walk post got me thinking about taking pictures of math things that I encounter everyday, but don’t really think about.

You already know that I work at the Belin-Blank Center on The University of Iowa campus.  But, you probably didn’t know that my office is on the top floor of the Blank Honors Center and that I have a straight shot at the Chemistry Building right out my window.

The other morning I was looking out my window, thinking about my math walk, and feeling inspired about taking pictures when I saw a student rushing into the Chemistry Building at about 9:03 (probably late for a 9am class).

That got me thinking. . . .I wonder how many students walk into the Chemistry Building on any given day?  And, I wonder what the ebb and flow of students looks like?

So, I took my first stab at time lapse photography (TLP).  Now, the primary purpose of this TLP project wasn’t to be artistic.  In fact, if you’re looking for an artistic TLP project you should go here.  The point of this project was to answer my second question; What’s the ebb and flow of students like outside my window everyday?

I set up a camera (and by “I”, I mean I asked someone I work with to help . . .she ended up doing while I stood in her office and watched!)  and programmed it to start snapping photos at 7:45 am and stop taking photos 12 hours later.  The camera took a picture every 15 minutes.  And, this is what I got:

Next, I graphed the flow of student traffic, based on the pictures I had.  The graph looked like this:

Chem Building Graph

Now, I’m wondering about quite a few things:

1. I wonder if I missed the busiest time of the day with my every 15 minute photo-shot?  It seems to me that at some point more than 18 students should be entering the Chemistry Building at one time.

2. What’s a good model for the data I collected?  Should I divide the graph into two (or more) separate parts . . .like day classes and evening classes?  Do I think these two times of day need to be modeled using two different equations?

3. Look at the shadows!  I wonder if I could try to plot the position of the sun or length of shadow vs. the time of day.

4. Given the structure of college courses I wonder how different the data would look if I collected data on a Monday or Wednesday?  Why might Friday not be a good data collection day?

What are some of the things you notice as you watch this TLP video?

Interested in creating your own?  I’d start here (actually, I did start there!).