Question

when you are comparing two sets of data, and one set is strongly skewed and the other is symmetric, which measures of the center and variation should you choose for the comparison?

Answer 1

In a skewed distribution, the median is the most central of the measures of central tendency.

Answer 2

The means and standard deviations

Answer 3

The mean and standard deviation are the best measure of center and spread for symmetriccal data (though still influenced by outliers), while the Median and IQR is best used for skewed data.

However:
When comparing distributions it is important to use the same measures of center and spread, defaulting to the median and IQR if any of the data is present.

(Info from Introductory Statistics: Exploring the World through Data, 3rd edition)

To answer your question, if one set is strongly skewed and the other is symmetric, you should use the median and IQR to measure center and variation.

Answer 4

Edit

However:
When comparing distributions it is important to use the same measures of center and spread, defaulting to the median and IQR if any of the data is skewed*** (typo).