Positive Skewness

Definition

Positive skewness is a statistical measure that describes the asymmetry of a probability distribution, where the right tail of the distribution is longer than the left tail. This indicates that the majority of the data values are concentrated on the left side of the distribution, with a few extreme values pulling the distribution to the right.

5 Must Know Facts For Your Next Test

1. Positive skewness indicates that the right tail of the distribution is longer, with the bulk of the data concentrated on the left side of the distribution.
2. Positively skewed distributions are often associated with data that has a lower bound but no upper bound, such as income, wealth, or certain types of measurements.
3. Outliers in a dataset can contribute to positive skewness, as they pull the distribution to the right.
4. Box plots are a useful tool for visualizing the skewness of a distribution, as the relative positions of the median, quartiles, and whiskers can indicate the presence and direction of skewness.
5. Positively skewed distributions can have implications for statistical analysis, as they may violate assumptions of normality and require the use of appropriate statistical methods.

Review Questions

• Explain how the shape of a positively skewed distribution differs from a symmetric distribution.
  • In a positively skewed distribution, the right tail of the distribution is longer than the left tail, indicating that the majority of the data values are concentrated on the left side of the distribution, with a few extreme values pulling the distribution to the right. This is in contrast to a symmetric distribution, where the left and right tails of the distribution are approximately equal in length, and the data is evenly distributed around the center.
• Describe the relationship between positive skewness and the presence of outliers in a dataset.
  • Outliers, or data points that lie an abnormal distance from other values in a dataset, can contribute to positive skewness. When there are a few extreme values that are much larger than the rest of the data, they pull the distribution to the right, resulting in a longer right tail and positive skewness. The presence of these outliers can have a significant impact on the shape of the distribution and the interpretation of statistical measures, such as the mean and standard deviation.
• Analyze how the information provided by a box plot can be used to infer the presence and direction of skewness in a dataset.
  • Box plots are a useful tool for visualizing the skewness of a distribution. In a positively skewed distribution, the median will be located to the left of the center of the box, and the whiskers (the lines extending from the box) will be longer on the right side, indicating the presence of a few extreme values pulling the distribution to the right. Additionally, the box itself will be asymmetric, with the distance from the median to the lower quartile being shorter than the distance from the median to the upper quartile. By examining the relative positions of the median, quartiles, and whiskers in a box plot, you can infer the presence and direction of skewness in the underlying dataset.

Related terms

Skewness:

Skewness is a measure of the asymmetry of a probability distribution. It can be positive, negative, or zero, indicating the direction and degree of asymmetry.

Box Plot:

A box plot is a graphical representation of a dataset that displays the median, quartiles, and potential outliers, providing information about the symmetry and skewness of the distribution.

Outliers:

Outliers are data points that lie an abnormal distance from other values in a dataset, often influencing the skewness of the distribution.