To calculate standard deviation, you’d compare each data point to the average to see how far apart they are, then average all the differences. Don’t worry – you won’t have to calculate standard deviation on your CPCU 500 test, but it is important to understand how the calculation works. Going back to the example above, since Store A’s sales are pretty consistent, the figures for each month aren’t going to be too far off from the annual average, so their standard deviation is going to be small. On the other hand, Store B is going to have big differences from month to month, so their standard deviation ends up being quite high, even though in the end, their average monthly sales is similar to Store A’s (so misleading!). Remember that with standard deviation, smaller is better because smaller standard deviation = less variation = more consistency & stability.
To give an example: let’s say you are going to award an athletic award at a school. One of the judging criteria is consistency in athletic performance, but your two top candidates are a basketball player & a swimmer. The basketball player averages 30 points per game, with a standard deviation of 15 points per game, and the swimmer has an average swim time of 1 minute per race with a standard deviation of 5 seconds per lap. Comparing the standard deviations of “15 points” to “5 seconds” doesn’t really tell you anything because they are completely different. If we use the coefficient of variation, however, we can see that the basketball player variation is 50% (15 points per game divided by average of 30 points per game) whereas the swimmer’s variation is only 8.3% (5 seconds per lap divided by average swim time of 60 seconds per race). Thus, having a percentage makes things easier to compare.
Fortunately, when it comes to the CPCU 500 exam, the focus is more on understanding the theory rather than making these statistical calculations. The main things you’ll need to know for the test are:
- Standard deviation
- used to compare variation among similar things (“apples to apples”)
- calculated by taking the average of all the differences between each data point compared to the overall average
- Coefficient of variation
- used to compare variation among dissimilar things (“apples to oranges”)
- calculated by taking standard deviation and diving by the mean or average
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