Statistics / Unit 2: Describing Distributions
2.6 Choosing Measures and Comparing Distributions
Notes
Skew and outliers affect the mean and standard deviation more than the median and IQR.
- A skewed distribution pulls the mean toward the tail. Skewed right: mean $>$ median. Skewed left: mean $<$ median. Symmetric: mean $\approx$ median.
- For skewed data or data with outliers, report the median and IQR. For roughly symmetric data, the mean and standard deviation work well.
- To compare distributions, discuss shape, center, spread and outliers in context, using comparison words such as "higher" or "more spread out".
- Example: salaries (in thousands) 40, 45, 50, 55, 160 have mean 70 and median 50. The 160 pulls the mean up.
Practice
Salaries (in thousands of dollars) are 40, 45, 50, 55, 160. Which is the better measure of a typical salary?
The mean is 70, higher than four of the five salaries. The median is 50.
A distribution is skewed left. Which statement is true?
The mean is pulled toward the long left tail.
The largest value in a data set of 9 values is increased by 1,000. Which statistic does NOT change?
The median is the 5th ordered value, and it does not depend on how large the maximum is.
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