Transcript

In this video, I would like to talk about variability. To begin we are going to take a look at a box of Smarties.

This box of Smarties says at the bottom that it contains 10 grams.  Do you think every box contains 10 grams? Let’s find out! 

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To weigh the Smarties, I am going to use this little weigh scale. What I will do is measure the box with the Smarties in it and then measure the empty box and find the difference. That will give me the weight of all the Smarties in the box.

So I have turned on the scale and I am going to put a box of Smarties on it. It says it weighs 11.9 grams. Now I am going to empty this box. So now I’m going to weigh the box, and it says two grams, which gives us 9.9 grams.

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As you can see, the weight is close to what it says on the box, but it is not exact.   Why is the Smarties not exactly 10 grams? To answer this question, let’s measure the weight of some individual Smarties.

So this Smartie weighs 1.0 gram. I have weighed nine different Smarties here, and you can see these Smarties do not all weigh the same. This means the weight of the Smarties shows variability.

So if I start filling up the box and were to aim for 10 grams, I would seldom hit the target exactly.  Instead I would either have to stop filling the box when the box weighed just less than 10 grams, or I would have to add one more Smartie and be just over my target.  That is why the box almost never contains exactly 10 grams.

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Objects can fall in a range of variability ranging from low to high.  For example these nuts and bolts here show a very low variability in there diameter. This is because the bolts should be able to fit in perfectly with the nuts.  In contrast to this pinecones can show a high variability in their lengths.  Lastly the weight of the Smarties would be somewhere in the middle.

The variability in data can be represented in various ways.  Some of the most common ways to measure variability include, range, variance and standard deviation.

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We are now going to discuss how to find the range of a set of data.  Range is the difference between the data’s maximum and minimum values, which in our case is the difference between the largest and smallest weighted Smartie.

To find range I need to find the difference between my maximum and my minimum value. So the maximum weight of Smartie is 1.2, and the minimum is 1.0. So this gives a difference 0.2 grams, and that is my range.

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Here is your homework: Find the length of your bedroom using a ruler. Re-measure the length of your room several times and see if you find variability in your findings.

To learn how to measure variability using variance and standard deviation be sure to watch the next video.

Thanks for watching EasyStats! Bye for now!