- Name the features of the distribution of a data set using statistical language
- Describe the connection between the distribution of a data set and its mean and median
Mean and Median Under Skew
Let’s see if we can choose the description that matches the shape of the data’s distribution, and then select the choice that gives the relationship between the mean and median for the data. Is the mean value impacted by the data’s distribution? Is the median value impacted by the data’s distribution?
Mean and Median for Skewed Distributions
- When the graph is skewed to the right, the mean will be greater than the median.
- When the graph is skewed to the left, the mean will be less than the median.
Resistance
Based on your answers to the question above, you might have noticed the direction the mean was pulled in under the skewness in the data set.
When a distribution is symmetric, the mean and median occupy the same value. But under a skew, the mean is “pulled” in the direction of the outliers: greater than the median in the case of positive (right) skew, and less than the median in the case of negative (left) skew. The value of the mean is affected by the presence of outliers and skew, while the median is not.