6.1 Bell Curves

By Susan, Bennett, and John

What Is A Bell Curve?

A Bell curve is a type of graph that includes a highest point, downward cup, and upward cups. The curve consists of points called inflection points, which transition when going up or down.

Properties of A Bell Curve

It is Bell-shaped, with highest point over the mean.
It is symmetrical with a vertical line going through the mean.
The curve approaches the horizontal axis but never touches or crosses it.
Transition points occur between upward and downward cups, about negative and positive means.

Examples

How to find the Mean and Standard Deviation on A Curve

On a bell curve the mean is the highest point. The lower point which does not touch the horizontal axis, usually equals 1.

The Empirical Rule

68% will lie within 1 standard deviation.
95% will lie within 2 standard deviation.
99.7% will lie within 3 standard deviation.

Rule Continued

Going further into the curve,

34% will lie between negative and positive 1 standard deviation.
13.5% will lie between negative and positive 2 standard deviation.
2.35% will lie between negative and positive 2 and 3 standard deviation.
0.15% will lie between negative and positive 3 standard deviation.

What Does Normal Distribution Mean?

Area under the entire distribution is 1.
Area over specific value randomly selected falls between A and B for example:

The distribution is symmetrical and mound-shaped and is centered over the mean.