This page would contain resource information like a glossary of terms from the section, key equations, and a reminder of concepts that were covered.
Make this more relevant to what students want — help them to build their processes, study guides, mnemonics, and memory dump material.
Essential Concepts
- The median stays relatively fixed in a dataset if one value changes by a large amount, the mean does not. This is indication that the mean is sensitive to the presence of extreme values in the dataset.
- When a distribution is symmetric, the mean and median occupy the same value. Under a skew, the mean is “pulled” in the direction of the outliers:
- Right-skewed: the mean is greater than the median.
- Left-skewed: the mean is less than the median.
- The mean, under certain conditions, can be a misleading indicator of a “typical” observation value.
Glossary
- right-skewed (positive skew)
- most of the data is bunched up to the left of the graph with a “tail” of infrequent values on the right (upper) end of the distribution.
- symmetric
- a distribution where the values are similarly distributed on either side of the mean/median.
- left-skewed (negative skew)
- most of the data is bunched up to the right of the graph with a “tail” of infrequent values on the left (lower) end of the distribution.
- resistant
- not affected by the skewness of a graph.
- outlier
- an unusual or extreme value, given the other values in the dataset.
Put formal DCMP I Can statements to prepare for the self-check.
These I Can Statements are new (the first three are the “you will understand” rephrased as an I Can):
- I can identify medians as being resistant to influence from skew and outliers.
- I can identify means as not being resistant to influence from skew and outliers.
- I can identify, in certain circumstances, when the mean is misleading.
- I can identify misleading claims made using means and suggest the most appropriate measure of center to use in different situations.
