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Different types of bells

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There are different types of “bells.” Although they look similar, each bell has two characteristics that distinguish it from other bells. These two characteristics are:

  • The position of μ on the number line.
  • The degree of curvature of the bell: is it narrow and high or wide and low?

Examples of differences in bells:

Example 1: Two bells with the same convexity but different positions:

Example 2: Two bells with the same position but different convexity

Two bells with the same position but different convexity:

Example 3: Two bells that differ from each other in two features: position and curvature.

The two bells differ from each other in two features: location and curvature.

The degree of curvature of the bell reflects the degree of dispersion of the distribution. The narrower and taller the bell, the more results are close to the expectation, and the meaning is low dispersion. The wider and lower the bell, the more dispersed the results. The statistical measure of the degree of dispersion is the standard deviation . Distributions with a small standard deviation reflect narrow and tall bells. Distributions with a large standard deviation reflect wide and low bells.

Normal curve obtained in samples

In the samples we will usually conduct, we will not obtain a normal curve that will be smooth and symmetrical like a bell. In most cases, the curve will only resemble a bell, and sometimes with great difficulty.
The distribution we obtain is called the sampling distribution. For example, if we measure the weight of fish in the Sea of ​​Galilee, we may obtain a distribution like this.