Coefficient of Variation: The coefficient of variation (CV) is a measure of relative variability or dispersion in a dataset. It is used to compare the variability of different datasets with different means and units of measurement. The coefficient of variation is expressed as a percentage.

To calculate the coefficient of variation, follow these steps:

1. Calculate the standard deviation of the dataset.
2. Calculate the mean of the dataset.
3. Divide the standard deviation by the mean.
4. Multiply the result by 100 to get the coefficient of variation as a percentage.

The formula for the coefficient of variation is:

Coefficient of Variation = (Standard Deviation / Mean) * 100

The coefficient of variation is particularly useful when comparing the variability of datasets with different scales or means. A higher coefficient of variation indicates a greater relative variability or dispersion.

Skewness: Skewness measures the asymmetry of a distribution. It quantifies the degree to which a dataset deviates from a symmetrical, bell-shaped distribution. Skewness provides information about the shape and the direction of the tail of the distribution.

Skewness can have three possible outcomes:

1. Positive Skewness: In a positively skewed distribution, the tail is elongated towards the right, and the majority of the data is concentrated on the left side of the distribution. The mean is typically greater than the median.
2. Negative Skewness: In a negatively skewed distribution, the tail is elongated towards the left, and the majority of the data is concentrated on the right side of the distribution. The mean is typically smaller than the median.
3. Zero Skewness: In a perfectly symmetrical distribution, the skewness is zero, indicating that the data is evenly distributed around the mean.

Skewness is often measured using different formulas, with one common formula being the Pearson’s coefficient of skewness.

Kurtosis: Kurtosis measures the degree of peakedness or flatness of a distribution in comparison to a normal distribution. It quantifies the presence of outliers or extreme values in a dataset. Kurtosis provides insights into the tails of the distribution and whether they are more or less extreme than those of a normal distribution.

Kurtosis can have three possible outcomes:

1. Leptokurtic: In a leptokurtic distribution, the data has a higher peak and heavier tails compared to a normal distribution. It indicates a larger number of outliers or extreme values.
2. Mesokurtic: In a mesokurtic distribution, the kurtosis is close to zero, indicating a distribution that is similar to a normal distribution in terms of peakedness and tail behavior.
3. Platykurtic: In a platykurtic distribution, the data has a lower peak and lighter tails compared to a normal distribution. It indicates a smaller number of outliers or extreme values.

Kurtosis is often measured using different formulas, with one common formula being the excess kurtosis, which measures the kurtosis relative to that of a normal distribution.

Both skewness and kurtosis provide insights into the shape and characteristics of a distribution and help in understanding the departure from a normal distribution.