Mean and Median Under Skew
effects of skew on mean and median
[Perspective video — a 3-instructor video that shows how to think about the tail and the two outliers in the data above together with the fact that the mean is larger than the median to begin to understand that the mean tends to be pulled to the right of the median under a right skew.]
For each of the plots of data below, 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 those data. Base your answers on the understanding you established in Questions 1 – 9 about the direction the mean was pulled in under the skewness in the data set.
question 10
Resistance
Resistant and Nonresistant Measures of Center
[Worked example – a 3-instructor video showing a symmetric data set with the mean and median identical, then, skewing the distribution to show what happens to the mean while the median remains in place.]
question 11
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.
