Wednesday, December 29, 2010

Introducing Graphs to Display Data

How we introduced  some of the various ways to display data with graphs went smoother this term.  The first types of graphs we cover are stemplots, dot plots, and histograms.  The textbook sort of whacks away at it with no rhyme or reason.  I wanted there to be a flow between the different types of graphs to help show why each might be needed.

We start the term with a video from the Against All Odds series by Annenberg called "What is Statistics." Before we watch I give the students a little pep talk on what we will be watching.  The video series is a little dated so I wanted to give the message of the video a chance before students tune out because of the 80's hairstyles, clothing, etc.  I tell them about the awesome 80's and they have seen a couple of "back in the day" photos of me already the first day of class.  I tell them to make mental notes of the of the style of the day because in twenty years they will get to look back at themselves and do the same.  I also mention the video is about how statistics is used.  After the video we chuckle about some of our favorite styles in the video but then chat about how the same thing is done now but with newer technology.  Talking points that get brought up are how websites seem to "know" you and Facebook applications.  How many "which friend do you know best?" quizzes have we taken?

In various scenarios the video basically shows people going through the scientific method.  The video focuses on the data collection and interpretation.  Using that as our backdrop we talk about dominant and non-dominate in regards to hand eye coordination.  We come to a general agreement that your dominant hand is supposed to be better.  The book has a penny stacking experiment where the class stacks with non-dominate and then compares to the "class" in the book results for dominate hand.  Where is the fun in that?  Since we have not even opened the book yet I comment I just happen to have a tub full of pennies we could stack.  From there we design our experiment to collect data.  Since this is our very first time designing an experiment we make all kinds of mistakes that we will get to talk about later.  They do a decent job pulling in their experience from various science classes.  We then do our experiment.

Here is where the fun starts.  We want to analyze our data to see if yes indeed our dominate hand is better at stacking pennies then our non dominate hand.  I have not had this happen yet, but to make sure the students do not get all fancy on me and organize themselves I have a few boys start us off by putting their results on the board.  Dominate hand on one side and non-dominate on the other.  The boys have so far done a nice job of using various font size, sideways, upside down, in other words making it look messy.  The rest of the class then joins in.  Once our data is on the board the question is posed.  Is our hypothesis correct?  A few students will take a stab at it.  We usually get conflicting arguments (remember we didn't design our experiment very well so it actually is not obvious which hand is better).  I then ask what's the big deal? Which hand is better?  Someone then suggests we organize our data.  A list is usually the first suggestion.  Even with a list we still have some difficulty.  By now the day is over and we will come back to it tomorrow.  At this time I have the students put their data in for me.  I have two computers in the room where I have a google form set up.  They just walk over and type in their info.

The next day I introduce a stemplot.  Afterwards our debate becomes easier.  Students are more confident in their opinions.  Another usual suggestion from earlier is to have a graph so a dot plot is introduced.  Again students are confident in their opinions using the dot plot to back it up.  Somewhere along the line there is usually the suggestion to have more data.  Since we did the experiment the day before I have all the hours written down.  Since they wanted more data I offer up the data from the other hours and have them add it to their dot plots.  After a few minutes of letting them work on the dot plots some grumbling begins and I stop the class and ask why all the not so happy faces?  Of course they talk about how it is annoying to put all those dots in and their dot plots are starting to look messy.

Cue the histogram.  We dive into histograms.  They like seeing how a bunch of dots become a "bin" for a histogram.  Our histogram is on the board and underneath each bin I will put a cup to help emphasize a bin is a collection of our dots.

As we introduced ourselves to the different graphs we are also discussing advantages and disadvantages of each.  I liked how each graph had a reason for being instead of the usual "here are the different graphs now go make them".

If you noticed we did not go back and debate dominate vs. non-dominate again using the histogram.  That will be our launch for the next topic, describing a distribution.

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