Skewness is a measure of the symmetry of a dataset. It describes the extent to which the values in the dataset are clustered around the mean. A dataset is considered symmetrical if the values on either side of the mean are roughly equal. If the values are not equal, the dataset is considered skewed.
There are two types of skewness: positive skewness and negative skewness. Positive skewness occurs when the majority of the values in the dataset are clustered on the left side of the mean, while negative skewness occurs when the majority of the values are clustered on the right side of the mean.
For example, consider the following two datasets:
Dataset 1: {1, 2, 3, 4, 5, 6, 7, 8, 9}
Dataset 2: {9, 8, 7, 6, 5, 4, 3, 2, 1}
The mean of Dataset 1 is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 5. The mean of Dataset 2 is (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) / 9 = 5. However, the distribution of the values in the two datasets is different. In Dataset 1, the values are evenly distributed around the mean, while in Dataset 2, the values are skewed to the right.
To calculate skewness, you can use the following formula:
Skewness = (3 * (mean – median)) / standard deviation
Where:
- mean is the mean of the dataset
- median is the median of the dataset
- standard deviation is the standard deviation of the dataset
Skewness can also be calculated using software such as Excel or a statistical software package.
Skewness is often used in statistical analysis to identify patterns or trends in the data and to make inferences about the underlying population. It is also useful for identifying outliers (extreme values) in the data and for identifying the appropriateness of statistical tests or models.
However, it’s important to note that skewness is not always easy to interpret and can be affected by the sample size and other factors. Therefore, it is often helpful to calculate and compare skewness for multiple datasets in order to get a better understanding of the data.
There are several properties of skewness that are useful to consider when analyzing data:
- Skewness is a measure of the symmetry of a dataset. A dataset is considered symmetrical if the values on either side of the mean are roughly equal. If the values are not equal, the dataset is considered skewed.
- Skewness can be positive or negative. Positive skewness occurs when the majority of the values in the dataset are clustered on the left side of the mean, while negative skewness occurs when the majority of the values are clustered on the right side of the mean.
- Skewness is affected by the presence of outliers (extreme values). A dataset with extreme values will generally have a higher skewness than a dataset without extreme values.
- Skewness is affected by the sample size. A larger sample size will generally have a lower skewness than a smaller sample size.
- Skewness is often used to identify patterns or trends in the data and to make inferences about the underlying population. It is also useful for identifying outliers in the data and for identifying the appropriateness of statistical tests or models.
- Skewness is not always easy to interpret and can be affected by other factors, such as the distribution of the data. It is often helpful to calculate and compare skewness for multiple datasets in order to get a better understanding of the data.
Overall, skewness is a useful measure of the symmetry of a dataset that can help you identify patterns or trends in the data and make inferences about the underlying population. However, it’s important to consider the properties of skewness and the limitations of this measure when analyzing data.