The Weight of a Feather Discrete or Continuous

Discrete Data vs Continuous Data

Transcript

Hi! Today we would like to talk about discrete and continuous data. To talk about discrete and continuous data, we have come to a local grocery store.

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Sometimes the things that we measure can take on only certain values. For example, a dice can generate one of the six outcomes namely the numbers between one and six. We say that these data take on discrete values.

In many ways, discrete distributions are comparable to integers because the values we measure take on only certain values.

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To illustrate this, we will weigh a few bottles of energy drinks using a scale. These bottles will give certain discrete weights depending on the number of bottles on the scale. So let's start with the blue one. Here we have four arrows showing the discrete values corresponding to the number of bottles that you will have on the scale at that time. As you can you can see, we got discrete values for the weights, only certain values and none of the values between them. This is because all of the bottles have the same weight and we weighed an integer number of them each time.

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At other times, the things we measure can take on any value within a certain range.  We call data of this kind continuous.  Continuous are more like real numbers then integers.

To illustrate continuous data, we are going to weigh some potatoes.  As you can see, potatoes seem to be able to take on any value within a range. If I weighed one hundred different potatoes I would expect that the results would be such that they could take on any value on the scale, meaning the value is continuous.

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As you might imagine, if I weighed out flour, or lentils, or a liquid, I could get any value on the scale, not just the discrete values I got when measuring the weight of one or more bottles.

Discrete and continuous data are fundamentally different from each other and they must be handled in different ways. You can see this easily if you try to make a histogram of two kinds of data we just measured.

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A histogram for the bottles weights is easy, we know exactly what the categories or bins should be.  They should be the discrete values that we observed during our experiment.  So for example, the first discrete value corresponds to the weight of one Gatorade bottle.  The second one corresponds to the two Gatorade bottles, and similarly the third one corresponds to three Gatorade bottles onto the scale.  And for the last one we have four bottles. And now we can make our histogram.

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Here I have the weight of ten different potatoes, and we got their weights at the grocery store. If the data are continuous like the weights of these potatoes we have to choose the division points or the bins used for the histogram and this should extend over the range of our weights over here. So now I'm going to use these values to plot my histogram over here. So my first potato weighs 626, so say my 626 is about over here.  My next potato weighs 422, which is about over here, and the next one 253…

So as you can see, the weights of our potatoes over here vary between a range and there are no two potatoes which have the same weight. So for each value within this range we could only find one potato.

I can count up the values in each of the bins and draw my histogram. So for example, this bin over here has two values between two hundred and three hundred, so I get a value of two over here. And I can do the same for the rest.

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Here is your homework: Find three examples of things that have variability. Explain whether each example is discrete or continuous. Then pose and try to answer a probability question about the likelihood of a particular outcome or a range of outcomes.

Thanks for watching! Bye for now!

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Source: http://www.civil.uwaterloo.ca/brodland/EasyStats/EasyStats/Discrete_vs_Continuous_Data.html

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