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What is the importance and usefulness of finding the mean/median/range/standard deviation?
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The importance and usefulness of looking at statistics about your data set is that you can determine whether or not the results are really representative of the data. The range will tell you how spread apart your data is. For example, let's assume we are working for Lego and we are studying how many Lego sets children own. If our study found that the mean is 10 sets, can we make the statement that the average child owns 10 sets?
We would need to look at the range. Let's say our range is 150. This means that the difference between the child with the most sets and the one with the least is 150. This shows that our data is not very close together. So, our "average" child is probably not that close to our mean answer of 10. Out data could be such that we have one really rich child that has 150 sets and the rest of the kids have 0, 1, 2. Could we really make the statement that the "average" child had 10 sets? No. We would then have to look at the median. The median is a more representative measure of the "average" when there are outliers (extreme numbers) involved. Let's say our median is 5. This means that when we cross out all of the extreme numbers and get to our center number it is 5. This sounds much more reasonable. This says that the "average" child has 5 Lego sets.
Another thing that we coudl look at is the standard deviation. This "normalizes" the data and gives us an idea of how far apart our data is from the mean. If we have a large standard deviation. This means that our data is farther from our mean. If we have a small standard deviation, that means that our data is closer to our mean.
All of this information is used to determine if our findings are valid or have "statistical significance." Another example is an election. Let's say that we find that 51% of the people surveyed are going to vote for Candidate A. We would need to look at the standard error for the survey. If our standard error is 5 points. That means, Candidate A could have 51 + 5 = 56% of the vote or 51 - 5 = 46% of the vote which could mean that we really don't know if the candidate will win or not. A famous U.S. Presidential election was forecast with the wrong winner due to something similar to this.
See the website listed below for additional information from a textbook.
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