Negatively Skewed vs. Positively Skewed

Attribute	Negatively Skewed	Positively Skewed
Mean	Less than the median	Greater than the median
Median	Greater than the mean	Less than the mean
Mode	Greater than the mean and median	Less than the mean and median
Tail direction	Longer tail on the left side	Longer tail on the right side
Distribution shape	Skewed to the left	Skewed to the right

Introduction

When analyzing data, it is important to understand the distribution of the data. Two common types of distributions are negatively skewed and positively skewed distributions. These distributions have different characteristics that can impact how we interpret the data. In this article, we will compare the attributes of negatively skewed and positively skewed distributions to better understand their differences.

Definition

A negatively skewed distribution, also known as left-skewed, is a type of distribution where the tail of the distribution is longer on the left side. This means that the majority of the data points are concentrated on the right side of the distribution, with fewer data points on the left side. On the other hand, a positively skewed distribution, also known as right-skewed, is a type of distribution where the tail of the distribution is longer on the right side. This means that the majority of the data points are concentrated on the left side of the distribution, with fewer data points on the right side.

Shape

One of the key differences between negatively skewed and positively skewed distributions is their shape. In a negatively skewed distribution, the peak of the distribution is shifted towards the right, with a long tail extending to the left. This indicates that there are more extreme values on the left side of the distribution. In contrast, in a positively skewed distribution, the peak of the distribution is shifted towards the left, with a long tail extending to the right. This indicates that there are more extreme values on the right side of the distribution.

Mean, Median, and Mode

Another important difference between negatively skewed and positively skewed distributions is the relationship between the mean, median, and mode. In a negatively skewed distribution, the mean is less than the median, which is less than the mode. This is because the tail of the distribution pulls the mean towards the left, away from the peak of the distribution. In a positively skewed distribution, the mean is greater than the median, which is greater than the mode. This is because the tail of the distribution pulls the mean towards the right, away from the peak of the distribution.

Interpretation

When interpreting data from a negatively skewed distribution, it is important to consider that the majority of the data points are clustered towards the right side of the distribution. This means that there are more low values in the data set, with fewer high values. In contrast, when interpreting data from a positively skewed distribution, it is important to consider that the majority of the data points are clustered towards the left side of the distribution. This means that there are more high values in the data set, with fewer low values.

Impact on Analysis

The skewness of a distribution can have a significant impact on the analysis of the data. For example, in a negatively skewed distribution, the mean may not be a good measure of central tendency because it is influenced by the extreme values on the left side of the distribution. In this case, the median may be a more appropriate measure of central tendency. On the other hand, in a positively skewed distribution, the mean may be a better measure of central tendency because it is influenced by the extreme values on the right side of the distribution.

Real-World Examples

Negatively skewed distributions are commonly seen in income data, where a small number of individuals earn extremely high incomes, pulling the mean income upwards. The majority of individuals earn lower incomes, resulting in a negatively skewed distribution. On the other hand, positively skewed distributions are commonly seen in test scores, where a small number of students score extremely high, pulling the mean score upwards. The majority of students score lower, resulting in a positively skewed distribution.

Conclusion

In conclusion, negatively skewed and positively skewed distributions have distinct attributes that impact how we interpret and analyze data. Understanding the shape, mean, median, and mode of these distributions is essential for making accurate conclusions based on the data. By recognizing the differences between negatively skewed and positively skewed distributions, researchers can make informed decisions about which measures of central tendency and variability are most appropriate for their data analysis.