Transcript

In the previous videos, we weighed ten Smarties and discovered variability in their weights. We also talked about some measures of central tendency and variability.  One of the most common measures of variability is variance.

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Some measures of variability such as range can give false impressions.  For example, in one of the previous videos I weighed these Smarties and I found out the range in their weights. Now say my one Smartie here weighed 2.5 grams instead of 1.1 gram. In that case my range will change to 2.5 minus 1.0, gives me 1.5. So this tells us that the weight of the Smarties vary by a range of 1.5 grams, but it fails to tell us that most Smarties here weigh around 1.0 grams and not 2.5 grams. This shows that range does not account for outliers like this. It’s not a very good measure for variability.

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A different and a very common measure of variability is called variance.  It is a bit difficult to calculate, but it gives a more trustworthy impression of most data.  This is because variance is a measure of how data is spread out around its mean. A low variance means that data points lie close to their mean and a high value means they are spread out.

One way to interpret variance is by thinking of it as the moment of inertia of a set of data. For example, say I have a body with an axis passing through its center point or its center of mass. The moment of inertia is the amount of force or torque required to rotate or cause angular acceleration on this body around its axis. The moment of inertia is dependent on how the mass is distributed around this axis.  For a set of data represented by this plot, the mean is the central point. The mean is equivalent to the center of mass.  My variance is dependent on how the data is spread out around the mean. So variance is equivalent to the moment of inertia. If I had another set of data which looked like this, then spread of data is less around the mean. This means the variance of this plot is less. A low variance means that data points lie close to their mean and a high value means they are spread out.

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Please join us in our next video to learn how to calculate variance. That’s it for now. Bye!