A symmetric distribution is not likely to have any outliers. A skewed distribution is much more likely to have them.
See solution.
Practice makes perfect
From the shape of a distribution, we can infer whether or not a data set has outliers and how they will affect the measures of center and variation. There are two main types of distribution shapes, symmetric and skewed. Let's analyze these one at a time.
Symmetric Distribution
A symmetric distribution has a peak that divides the data evenly. The data on the right is approximately a mirror image of the data on the left. Outliers are not common in this type of distribution.
Since the mean and standard deviation use all the data values, these measures best describe a symmetric distribution.
Skewed Distribution
In a skewed distribution, the peak is on the right or the left, and most of the data is around it. This distribution is likely to have outliers in the tail of the graph. The outliers will affect the mean and standard deviation.
Since the five-number summary is less affected by outliers, these measures are preferred to describe skewed distributions.
Conclusion
When we know the shape of a distribution, we can quickly also know which measures best describe the data.
Symmetric:&Mean and Standard Deviation
Skewed:&Five-Number Summary
