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?
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.
In a skewed distribution, the median is the most central of the measures of central tendency.
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).
When comparing two sets of data, one that is strongly skewed and the other that is symmetric, it is important to choose measures of center and variation that are suitable for each type of distribution.
For the set of data that is strongly skewed, the median is a more appropriate measure of center compared to the mean. This is because the median resists the influence of extreme values and is a robust measure of central tendency. You can find the median by arranging the data in ascending order and identifying the middle value. Alternatively, if there is an even number of data points, you can take the average of the two middle values.
On the other hand, for the set of data that is symmetric, both the mean and median can be effective measures of center. In this case, the mean provides a good estimate of the central tendency as it takes into account all the data values. However, if there are outliers present, the median may be a more suitable measure since it would not be affected by extreme values.
When it comes to measuring the variation in the data, the most common measure used is the standard deviation. The standard deviation provides a measure of how spread out the data is from the mean. It is generally applicable to both skewed and symmetric distributions, as long as the mean is used for the central tendency measure. Standard deviation allows you to quantify the dispersion of data points around the mean, indicating if the data is tightly clustered or widely spread.
In summary, when comparing two sets of data, one strongly skewed and the other symmetric:
- Use the median as the measure of center for the strongly skewed data.
- Use either the mean or median as the measure of center for the symmetric data, depending on the presence of outliers.
- Use standard deviation as the measure of variation for both types of data, ensuring that you have used an appropriate measure of center.