Range of Data

While the Measures of Central Tendency are about determining central tendencies of data, the range of data is about how the data spreads or disperses. So while it is useful to know that the mean of the police case load by week in Boston is 300, it is also very useful to know if it's within 10 cases of 300 every single week, or if the numbers fluctuate wildly and it can go from 200 cases one week to 400 cases the next week. The distance between the high and low point is the range.

The range is useful in all sorts of applications. If you're looking at weather for Boston in January, you might hear that it has a mean of 35F. But does this mean that it's always pretty much 35F? Or does that mean that sometimes it can be as high as 60F and at other times it can be down at -20F? It would be fairly important for someone moving to the area to know what the full range of temperatures can be, since just looking at the mean could be very misleading.

Let's say you're an editor at BellaOnline and sending me email messages. You might know that my mean of responding is 3 days. But this could actually mean that many messages I respond to in 10 minutes because they're quick - and that other messages I take 3 weeks to respond to because they involve effort and they get put onto my to-do list. If all you have in mind is that 3 days is a mean, you could be fairly disappointed when six days have passed without a reply. You have a much better idea of what will happen by knowing the range.

To take it a step further, what if my email response times weren't evenly distributed around this window of 10 minutes to 3 weeks? What if most of my responses were somewhere between 2-4 days and it was only rarely that I had a response time outside that window? That is where the variance and standard deviation come in. These measures help to figure out where the clusters are in a group of numbers. That way, instead of an editor just knowing "responses can come in anywhere in the range of 10 minutes to 3 weeks", they get to know "you can probably expect an answer within 2-4 days, but please know that it is possible for the answer to come in the range of 10 minutes to 3 weeks". That way they know both the higher probability of what will happen - as well as the full possibilities.

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