population the definition of the distribution of a data population. Also, find the statistic that measures the width of dispersion (looseness or tightness) of the population data around its mean. give an example of the type of situation where this statistic might be critical to making good decisions about the population under study

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#5, I believe airline seats -- at least in economy class -- are getting smaller, and airlines are not really making any concessions for XL passengers. This is a constant debate on Frommers.com. A quick search gives me this and this; there might be more recent information. The last time I flew, it was in economy, and I was quite encroached by my seatmate; fortunately I had the aisle seat so I could lean over a little more. I'm starting to advocate for trains.

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A very recent topical example is the size of seats in aeroplanes, and the way that American airlines have been forced to make their seats larger in response to the increase in obesity and overweight people in America. This is of course an excellent example of where standard deviation can change, and how society has to change to accommodate this alteration.

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A set with a high standard deviation is "spread out" more than a set with a low standard deviation.  You can calculate the standard deviation by finding the difference between each data value and mean, squaring these differences, taking the average, then square rooting.  But the main thing to know is that higher SD = more spread out.

Say you're looking at two investment options, which each claim to double your money in 10-30 years, with a mean of 20 years.  Option A has a very small standard deviation, while Option B has a large SD.  This means that Option A is more of a "sure thing" shortly after 20 years, while Option B is more of a risk...

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Another example of a situation where understanding the distribution of the sample population and the standard deviation within that range:

Designers of home exercise equipment need to look at the full range of height, weight, strength, endurance, and other characteristics of the potential customers for their equipment. However, it is not practical or possible to always design home-use equipment for the extremely short or morbidly obese individual, for example. By researching the standard deviations of body types and sizes, the manufacturers can determine the design capacity that will allow their equipment to be workable for the widest practical range of customers.

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I believe that the statistic you are talking about is standard deviation.  The whole point of standard deviations is that they show you how far from the mean various percentages of your data are likely to fall.  The more dispersed your data, the bigger the standard deviation.

As for the second part of your question, it really depends on what you're planning to do with your information.  For example, if you're measuring body size and you want to make one-size-fits-all chairs, it's pretty important to know if your population clusters around the mean or if you've got really big and really small people.

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