3 ms·

Given outliers in a skewed dataset, wouldn't median be a worse description than mean without outliers? https://openstax.org/books/statistics/pages/2-6-skewness

by adolph 3y ago

Given outliers in a skewed dataset, wouldn't median be a worse description than mean without outliers? https://openstax.org/books/statistics/pages/2-6-skewness-and-the-mean-median-and-mode https://openstax.org/books/statistics/pages/2-6-skewness-and...

ghufran_syed 3y ago
I think the median works better in this situation because the huge population means that both the outliers and the skewness have much less effect than they do on the mean. The problem with using the mean “without outliers” is that you have to make arbitrary decisions about what data to exclude as an outlier, unlike with the median.
sapiogram 3y ago
The answer is always "it depends", which is exactly why I prefer the median in most cases. Once you choose to use the median, there are no more choices/degrees of freedom - it's just the median. On the other hand, "mean without outliers" requires you to make a subsequent value judgement on what exactly is an "outlier".
- adolph 3y ago
  > "mean without outliers" requires you to make a subsequent value judgement Do you think that comparison of outliers to interquartile range is not a relatively objective method of determining outliers? The interquartile range is a number that indicates the spread of the middle half, or the middle 50 percent of the data. It is the difference between the third quartile (Q3) and the first quartile (Q1) . . . The IQR can help to determine potential outliers. A value is suspected to be a potential outlier if it is less than 1.5 × IQR below the first quartile or more than 1.5 × IQR above the third quartile. Potential outliers always require further investigation. https://openstax.org/books/statistics/pages/2-3-measures-of-the-location-of-the-data https://openstax.org/books/statistics/pages/2-3-measures-of-...

3 ms·

Given outliers in a skewed dataset, wouldn't median be a worse description than mean without outliers? https://openstax.org/books/statistics/pages/2-6-skewness

by adolph 3y ago

ghufran_syed 3y ago
I think the median works better in this situation because the huge population means that both the outliers and the skewness have much less effect than they do on the mean. The problem with using the mean “without outliers” is that you have to make arbitrary decisions about what data to exclude as an outlier, unlike with the median.
sapiogram 3y ago
The answer is always "it depends", which is exactly why I prefer the median in most cases. Once you choose to use the median, there are no more choices/degrees of freedom - it's just the median. On the other hand, "mean without outliers" requires you to make a subsequent value judgement on what exactly is an "outlier".
- adolph 3y ago
  > "mean without outliers" requires you to make a subsequent value judgement Do you think that comparison of outliers to interquartile range is not a relatively objective method of determining outliers? The interquartile range is a number that indicates the spread of the middle half, or the middle 50 percent of the data. It is the difference between the third quartile (Q3) and the first quartile (Q1) . . . The IQR can help to determine potential outliers. A value is suspected to be a potential outlier if it is less than 1.5 × IQR below the first quartile or more than 1.5 × IQR above the third quartile. Potential outliers always require further investigation. https://openstax.org/books/statistics/pages/2-3-measures-of-the-location-of-the-data https://openstax.org/books/statistics/pages/2-3-measures-of-...