Positively Skewed

Definition

Positive skewness, or a positively skewed distribution, refers to a distribution where the right tail of the graph is longer than the left tail, resulting in the mean being greater than the median. This asymmetrical shape indicates that the majority of the data is concentrated on the left side of the distribution, with a longer right tail containing outliers or extreme values.

5 Must Know Facts For Your Next Test

1. In a positively skewed distribution, the mean is greater than the median, which is greater than the mode (mean > median > mode).
2. Positively skewed distributions are common in real-world data, such as income, wealth, and the size of various objects or organisms.
3. Positive skewness indicates that the data has a longer right tail, with more extreme high values compared to the bulk of the data on the left side.
4. Positively skewed distributions are often associated with growth processes, where small changes accumulate over time to produce large values.
5. Skewness can be quantified using a statistical measure called the skewness coefficient, which takes a value of zero for a symmetric distribution, positive for a positively skewed distribution, and negative for a negatively skewed distribution.

Review Questions

• Explain how the mean, median, and mode are related in a positively skewed distribution.
  • In a positively skewed distribution, the mean is greater than the median, which is greater than the mode (mean > median > mode). This is because the longer right tail of the distribution, containing the extreme high values, pulls the mean to the right, away from the median. The mode, being the most frequent value, is located on the left side of the distribution, closest to the bulk of the data.
• Describe the relationship between skewness and the shape of the distribution.
  • Positive skewness indicates that the distribution has a longer right tail, with more extreme high values compared to the bulk of the data on the left side. This asymmetrical shape is in contrast to a symmetric distribution, where the tails on both sides of the mean are equal in length. The degree of skewness can be quantified using the skewness coefficient, which takes a positive value for a positively skewed distribution, zero for a symmetric distribution, and negative for a negatively skewed distribution.
• Analyze the potential causes and real-world examples of positively skewed distributions.
  • Positively skewed distributions are commonly observed in natural and social phenomena where small changes accumulate over time to produce large values, such as income, wealth, the size of various objects or organisms, and growth processes. These distributions are often associated with multiplicative processes, where the outcome is the product of many independent factors. Understanding the causes and characteristics of positively skewed distributions can provide valuable insights in fields like economics, biology, and social sciences, where these patterns are prevalent.

Related terms

Skewness: Skewness is a measure of the asymmetry of a probability distribution. It describes the degree and direction of asymmetry around the mean of a distribution.

Median: The median is the middle value in a sorted list of numbers, where half the values are above the median and half are below.

Mode: The mode is the value that appears most frequently in a dataset. In a positively skewed distribution, the mode is typically less than the median.