The Value of Variance

More often than not, when we are presented with statistics we are given only a measure of central tendency (such as a mean). However, lots of useful information can be gleaned about a dataset if we examine the variance, skew, and the kurtosis of the data as well. Choose a statistic that recently came across your desk where you were just given a mean. If you can't think of one, come up with an example you might encounter in your life. How would knowing the variance, the skew, and/or the kurtosis of the data give you a better idea of the data? What could you do with that information?

Example: Say you are an executive in an automobile manufacturer, and you are told that, for a particular model of new car that you sell, buyers have on average 2.2 warrantee claims over the first three years of owning the car. What would additional information on the shape of your data tell you? If the variance was low, you'd know that just about every car had 2 or 3 warrantee claims, while if it was high you'd know that you have a lot of cars with no warrantee claims and a lot with more than 2.2. The skew would provide similar information; with a high level of right skew, you'd know that the average is being brought up by a few lemons; with left skew you'd know that very few of the cars have no warrantee claims. The kurtosis (thickness of the tails) would help you get an idea as to just how prevalent the lemon problem is. If you have high kurtosis, it means you have a whole bunch of lemons and a whole bunch of perfect cars. If you have low kurtosis, it means that you have few lemons but few perfect cars.