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Video:What is a Bell Curve?

with Ben Owens

Bell curves are a graphical representation of what is known as normal distribution in statistics. Learn more about the bell curve and the theory behind it in this About.com video.See Transcript

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Transcript:What is a Bell Curve?

Hi, I’m Ben Owens, math educator - here for About.com to explain the bell curve!

Normal Distribution Forms a Bell Curve

 This is a bell curve, as you can see it kind of looks like... a bell, hence the name.  We encounter the bell curve in statistics and basically it is the graphical representation of what we call the Normal Distribution. So when do we see the bell curve?

Histograms to Find Bell Curves

 When we are given a bunch of data, one way to see how the data look is to use a histogram.  The histogram shows how the data are distributed.  Often when the histogram is made, we see that the data follow this basic shape.   For instance, say I give a math test to one of my math classes, and I want to analyze the results. I just write down the 10 point ranges, from 50 to 59, 60 to 69, 70 to 79, and so forth -- and tally all the test scores behind them. Often times, this kind of shape appears. A few students do very well, a few do very poorly, and a bunch of scores are pretty similar, right in in the middle. That’s the bell curve. 

Important Features of a Bell Curve

 So, here are some important features of bell curves that distinguishes them from other curves in statistics. First of all, the modal class on the bell curve right here in the middle and it coincides with the mean and the median. You can find that in the highest part of the curve, right here.

A bell curve should also be symmetric, so if you divide the curve up in half, both halves are mirror images of each other.  Thus 50% of the data are above the average and 50% are below the average. So, a shape that’s higher at the end, like this one, is not a bell curve. And then, a bell curve follows the 68-95-99.7 rule. It’s basically an easy way to make calculations on the bell curve. About 68 percent of all the data should be within one standard deviation of the mean. About 95 percent of all the data should be within two standard deviations of the mean. And about 99.7 percent of all data should be within three standard deviations of the mean. 

Maybe the coolest place where we see the Bell Curve is in what is called the Central Limit Theorem. For more on the mean, standard deviation and the bell curve, visit us at education.about.com. Thanks for watching!

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