Asymmetry or aiming measurement

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Asymmetry or aiming measurement

Classification

-If the result after applying the formula is less than zero, it is called Negative Asymmetry.

-If the result after applying the formula is greater than zero, it is Positive Asymmetry.

-If the result after applying the formula is zero, it is called Symmetric.

Utility

Many simplistic models assume a normal distribution, that is, symmetric about the mean. The normal distribution has zero skewness. As the sample size increases, any population tends to become symmetric. A positive skewness implies that there are more distinct values to the right of the mean.

formulas

- The Bowley-Yule skewness coefficient:

this calculation is based on the median and quartiles. If the distribution is symmetric, the first and third quartiles will be located at the same distance from the median. This will give the result that the skewness is equal to 0. On the other hand, if the skewness is positive, the result will be greater than 0. If it is negative, this value will be less.

-Fisher's asymmetry coefficient:

this method is a little more complex and is based on the deviations that the observed values present with respect to the mean. It is calculated by dividing the third moment by the standard deviation.

-The second Pearson skewness coefficient:

it is another average that is used to determine the skewness of a data set. To perform this calculation, the mode must be subtracted from the median. Next, we multiply the result by three and divide the result by the standard deviation.

-Pearson's first skewness coefficient:

this is a measure of skewness that consists of subtracting the mean from the mode and dividing the difference by the standard deviation of the data. It is mainly used in unimodal distributions.

Characteristic

- It can be determined by how the mean, median, and mode of a distribution are related to each other.

-You can have a curve skewed to the right or left (positive or negative asymmetry).

What are they?

They are indicators that allow establishing the degree of symmetry (or asymmetry) that a probability distribution of a random variable presents without having to make its graphic representation.