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Working with limited data

Please help me with the attached document. I do not know how or where to begin.

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 and the skew of the data give you a better idea of the data? What could you do with that information?

Here is an 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.


Solution Preview

One possible example would be the returns of a specific stock (say, General Motors). Let's say you are told that, over the last 40 years, the average yearly return of this stock has been 10%. Then:

- Knowing the variance would give you an idea of the "risk" of this stock. For example, if it had very low variance, you'd know that the General Motors stock returns were very close to 10% ...

Solution Summary

The solution provides a real-life example in which knowing the skewness of a distribution is important for making decisions.