What are the chances we’ll have to wait only an hour to see it? What about two hours? Is there any chance we have to wait three hours? Let’s think through this using the Empirical Rule.įirst, let’s fill in the distribution of #s of minutes it takes the geyser to erupt, according to the Empirical Rule. Let’s assume a standard deviation of 15 minutes, and a normal distribution of times between eruptions. Suppose we are thinking about visiting the famous Old Faithful geyser in Yellowstone National Park, and we want to be sure that we catch the geyser erupting, which it does every 90 minutes, on average. Let’s think through some examples to make this more concrete and start seeing how cool and useful this rule is. It’s certainly possible, but the chances are very small. These are very small percentages (0.1%), though, which tells us that there are very rarely any scores this far away from the mean in a normal distribution. Notice that there are some scores indicated in the graph that fall outside of the range of -3σ to 3σ. This matches up with the “about 99.7%” we have listed in the Empirical Rule percentages above. And if we sum up the four sections in that range of -2σ to 2σ, 13.6% + 34.1% + 34.1% + 13.6%, we indeed get a sum of 95.4%. Next, moving out to two standard deviations away (all the space between -2σ to 2σ on the graph), the Empirical Rule said that should total up to about 95% of all scores. The Empirical Rule tells us we should see that about 68% of all possible scores will fall within 1 standard deviation of the mean (either above it or below it) this matches up with the 34.1% plus 34.1% we see from -σ to σ in the two middle sections on the graph. In this illustration, we’ve got a more detailed breakdown of the same percentages we have listed up above, so let’s talk through how they match up. Each of those sections represent the distance of one population standard deviation (little sigma, σ) away from a population mean, mu (Μ). Here, we’ve got our normal distribution like we’ve seen before, but now we’ve added six equal sections marked off using vertical lines. You will want to remember those values because we’ll see just how useful they are. The Empirical Rule is also sometimes called the 68-95-99.7 rule, because it provides those percentages noted above. and 99.7% or nearly all scores will fall within 3 standard deviations of the mean.about 95% of all scores will fall within 2 standard deviations of the mean.about 68% of all scores will fall within 1 standard deviation of the mean (that is, within 1 standard deviation above or below the mean).The Empirical Rule tells us that, if we have normally distributed data, then the following will be true: Let’s talk about one of the coolest applications of standard deviation – the Empirical Rule.
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