Q&A #10489

Graphing: discrete vs continuous data

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From: Jeanne (for Teacher2Teacher Service)
Date: Feb 07, 2003 at 20:32:15
Subject: Re: Graphing: discrete vs continuous data

>As Mrs. Shidell wrote to Dr. Math
>On 02/04/2003 at 12:13:46 (Eastern Time),
>>I am using the Connected Math series from Prentice Hall.  The 
>>is Variables and Patterns.  Students are learning coordinate
>>graphing.  The teacher's manual doesn't make it clear when to 
>>the points in the line and when not to.  However, the question is
>>repeated throughtout the text, "Is it appropriate to connect the
>>points?"  I'm having a hard time explaining this concept to seventh
>>graders.  Can you help?
>>Thank You,
>>Mrs. Shidell
>>Grade 7 Plainfield Central School
>>The information in the manual isn't clear or doesn't seem consistent.
>>In once instance, bicyclists miles are being plotted on a graph with
>>time on the x axis, and miles on the y.  The points are connected.
>>In the next problem, bicyclists are traveling away from a particular
>>city.  Again time is on the x, and miles on the y.  However, in this
>>case, the points are not connected.  The explanation given is that
>>it's the miles away from the city that is being graphed, not the
>>number of miles traveled by the cyclists.  This isn't clear to me.

Hello Linda,

The questions are asking the students about the concept of "discrete 
vs continuous" data.

Let's look at some data I've made up for the sake of explanation:

Suppose I have a ball, I drop it from a height of 100 cm and let it bounce 4 
times.  The data I want to collect is height reached after each bounce and I 
want to graph this data.

          Starting ht:        100 cm
          After bounce #1:     80 cm
          After bounce #2:     64 cm
          After bounce #3:     51 cm
          After bounce #4:     41 cm

My x-axis would be the bounce number. My y-axis would be the height in 
centimeters. In this graph, I would NOT connect the dots.  If I draw a line 
segment connecting the (1,80 cm) and the (2,64 cm) dots, the line 
segment implies that there exists data representing bounces between 
the 1st and the 2nd bounce.  Since a "fractional bounce number" 
doesn't exist.  We should not connect the dots.  This is an example of 

Let's change the situation slightly.  The data I want to collect is the 
distance traveled by this ball over time.  To make this example easier, let's 
assume it takes 1 second to travel from the initial drop to the 1st bounce, 
and 1 second to travel between each of the subsequent bounces.  
Here's data.

     time     1 sec.           distance:  100 cm
              2 sec.                      260 cm  (100 + 80 + 80)
              3 sec                       388 cm  (100 + 80 + 80 + 64 + 64)
               etc                          etc.

My x-axis would represent time in seconds and my y-axis would represent the 
distance traveled in cm.  In this graph I WOULD connect the dots. The segment 
connecting the (1,100) and the (2,260) implies that there exists data between 
1 second and 2 seconds.  That is, there is a distance that can be measured 
when the ball travels for any number between 1 and 2 seconds.  This is an 
example of CONTINUOUS data.

When I taught this concept to my students, I'd ask something like "does 
there exist [non-whole number] of _____?"  For example,  "does there 
exist 1 1/2 bicyclists?"  or "can we travel 2 2/3 miles?"  or "is there such 
a thing as 4.2 cars?"  We'd use this kind of question to help us decide 
whether data is discrete or continuous (whether to connect the dots or not).

Hope this helps.
 -Jeanne, for the T2T service

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