Skewness

Skewness is a measure of the asymmetry of the probability distribution of a random variable. A distribution is skewed if it is not symmetric around its mean.

The skewness of a distribution can be positive or negative. A distribution with a positive skew has a longer tail on the right side of the mean, while a distribution with a negative skew has a longer tail on the left side of the mean.

The skewness of a distribution can be calculated using the following formula:

```
Skewness = (Mean - Median) / Standard Deviation
```

The mean is the average of the values in the distribution, the median is the middle value of the distribution, and the standard deviation is a measure of the spread of the values in the distribution.

Skewness can be used to identify distributions that are not normally distributed. A normal distribution is a symmetric distribution that is bell-shaped. The mean, median, and mode of a normal distribution are all equal.

Distributions that are skewed can be more difficult to analyze than normal distributions. This is because the mean and median of a skewed distribution are not equal, and the standard deviation is not a good measure of the spread of the values in the distribution.

Skewness can be caused by a number of factors, including the presence of outliers in the data, the type of distribution, and the sample size.

Outliers are data points that are significantly different from the rest of the data in the distribution. Outliers can cause a distribution to be skewed.

The type of distribution can also affect the skewness of a distribution. Some distributions, such as the log-normal distribution, are inherently skewed.

The sample size can also affect the skewness of a distribution. Smaller sample sizes are more likely to produce skewed distributions than larger sample sizes.

Skewness is an important concept in statistics. It can be used to identify distributions that are not normally distributed and to understand the causes of skewness.