Question Video: Recalling the Areas under a Normal Distribution Curve | Nagwa Question Video: Recalling the Areas under a Normal Distribution Curve | Nagwa

Question Video: Recalling the Areas under a Normal Distribution Curve Mathematics • Third Year of Secondary School

For a normally distributed data set, approximately what percentage of data points will lie within one standard deviation of the mean?

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Video Transcript

For a normally distributed data set, approximately what percentage of data points will lie within one standard deviation of the mean?

The graph of a normal distribution is a bell-shaped curve, and it’s completely symmetrical about the mean. The area beneath the curve is one, or 100 percent. And we model our data by considering its distance from the mean in terms of the standard deviation 𝜎. And this is sometimes called the 68-95-99.7 rule. It tells us that approximately 68 percent of data points will lie within one standard deviation of the mean. And then approximately 95 percent of data points lie within two standard deviations of the mean. And finally, approximately 99.7 percent of data points lie within three standard deviations of the mean.

Using the 68-95-99.7 rule, we can say that for one standard deviation in a normally distributed data set, 68 percent of the data points will lie within one standard deviation of that mean.

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