Statistics

Bell Shaped Curve

There are various types of bell-shaped curves.

They look similar, but each bell-shaped curve has two characteristics that differentiate it from the other bell-shaped curves. These characteristics are as follows:

  1. The location of μ on the number axis.

  2. The degree of convexity of the curve (i.e., whether it is narrow and high, or wide and low).


Example 1: Two bell-shaped curves with the same convexity, but different locations relative to μ .

Diagram

Different Types of Bell-Shaped Curves-1

 

Example 2: Two bell-shaped curves with the same locations relative to μ, but different degrees of convexity.

Diagram

Different Types of Bell-Shaped Curves-2

 

Example 3: Two bell-shaped curves with the same locations relative to μ, but different degrees of convexity.

Diagram

Different Types of Bell-Shaped Curves-3

 

The degree of convexity of a bell-shaped curve reflects the degree of dispersal of its probability distribution. The narrower and higher the bell-shaped curve, then the closer most of the results will be to the expectation, which means less dispersal. The wider and lower the bell-shaped curve, then the more widely dispersed the results will be The statistical measure of the degree of dispersal reflects the standard deviation. Probability distributions with a low standard deviation reflect narrower and higher bell-shaped curves, while probability distributions with a high standard deviation reflect wider and lower bell-shaped curves.

Bell Shaped Curve 527Bell Shaped Curve