Negative Skew vs. Positive Skew

Attribute	Negative Skew	Positive Skew
Mean	Less than Median	Greater than Median
Median	Greater than Mean	Less than Mean
Mode	Greater than Mean and Median	Less than Mean and Median
Tail direction	Left	Right
Frequency distribution	More values on the right side	More values on the left side

Definition

Negative skew and positive skew are two terms used in statistics to describe the shape of a distribution. Skewness refers to the asymmetry of the distribution around its mean. A distribution is said to have negative skew when the tail on the left side of the distribution is longer or fatter than the tail on the right side. Conversely, a distribution is said to have positive skew when the tail on the right side of the distribution is longer or fatter than the tail on the left side.

Characteristics of Negative Skew

When a distribution has negative skew, it means that the majority of the data points are concentrated on the right side of the distribution, closer to the mean. The tail on the left side of the distribution is longer, indicating that there are some extreme values pulling the mean to the left. In a negatively skewed distribution, the median is typically greater than the mean, as the mean is being pulled down by the extreme values on the left side.

• Negative skew indicates that the distribution is not symmetrical.
• The mean is less than the median in a negatively skewed distribution.
• Negative skew can be caused by outliers on the lower end of the distribution.
• Negative skew can affect the interpretation of the data, as it may indicate that the majority of the data points are below the mean.
• Negative skew can be adjusted by transforming the data or removing outliers.

Characteristics of Positive Skew

On the other hand, when a distribution has positive skew, it means that the majority of the data points are concentrated on the left side of the distribution, closer to the mean. The tail on the right side of the distribution is longer, indicating that there are some extreme values pulling the mean to the right. In a positively skewed distribution, the mean is typically greater than the median, as the mean is being pulled up by the extreme values on the right side.

• Positive skew indicates that the distribution is not symmetrical.
• The mean is greater than the median in a positively skewed distribution.
• Positive skew can be caused by outliers on the higher end of the distribution.
• Positive skew can affect the interpretation of the data, as it may indicate that the majority of the data points are above the mean.
• Positive skew can be adjusted by transforming the data or removing outliers.

Comparison

While negative skew and positive skew both indicate that a distribution is not symmetrical, they differ in the direction of the skewness. Negative skew indicates that the tail on the left side of the distribution is longer, while positive skew indicates that the tail on the right side of the distribution is longer. In terms of the relationship between the mean and the median, negative skew results in a mean that is less than the median, while positive skew results in a mean that is greater than the median.

Both negative skew and positive skew can be caused by outliers in the data. Outliers on the lower end of the distribution can lead to negative skew, while outliers on the higher end of the distribution can lead to positive skew. In both cases, the presence of outliers can affect the interpretation of the data, as they pull the mean in the direction of the skewness.

When it comes to adjusting for skewness, both negative skew and positive skew can be addressed by transforming the data or removing outliers. Transformations such as logarithmic or square root transformations can help make the distribution more symmetrical. Removing outliers can also help reduce the impact of extreme values on the skewness of the distribution.

Conclusion

In conclusion, negative skew and positive skew are two important concepts in statistics that describe the asymmetry of a distribution. While negative skew indicates a longer tail on the left side of the distribution and a mean less than the median, positive skew indicates a longer tail on the right side of the distribution and a mean greater than the median. Both types of skewness can be caused by outliers in the data and can be addressed by transforming the data or removing outliers. Understanding the characteristics of negative skew and positive skew is essential for interpreting and analyzing data effectively.