IDL was created in the 1980's. Believe it or not, back then the current idea to average the two middle values for datasets with an even number of elements to obtain the median was not standard practice. This idea seems to have emerged in the early 1990's.

The Numerical Recipes 2nd Edition book was used to formulate much of core IDL back in the 1980's and 1990's. This book was cutting-edge for its time and described how to use computer code for science! A funny quote about median calculations from this book follows...

"One often wants to know the median element in an array, or the top and bottom quartile elements. When N is odd, the median is the kth element, with k = (N + 1)/2. When N is even, statistics books define the median as the arithmetic mean of the elements k = N/2 and k = N/2+1 (that is, N/2 from the bottom and N/2 from the top). If you accept such pedantry, you must perform two separate selections to find these elements. For N > 100 we usually define k = N/2 to be the median element, pedants be damned."

See Section 8.5 on Page 333 for more information: https://websites.pmc.ucsc.edu/~fnimmo/eart290c_17/NumericalRecipesinF77.pdf

So in summary, yes the accepted method to average the two middle elements is now technically correct, and has been for the last ~30 years. However, in order to maintain backwards compatibility, this "new" method was only included in IDL through the optional EVEN keyword.

Hope this helps!

Hi Ben,

Thanks for the information on this - I never knew that was the commonly accepted way of doing it back in the 80's/90's.

Regarding my data - do you think it's something I need to re-process using /EVEN, or do you think it's perfectly fine to say I've used MEDIAN without the EVEN keyword? I'm happy to give more information if you'd like.

Cheers

The "lazy" approach to median derivation 30+ years ago was rooted in the computational expense to locate two numbers and then average them, rather than just locating one number.

I am not a statistics expert, but the answer to your re-processing question will depend on the range of your data and more importantly, how many data values are involved. If you only have 6 data points, it would likely be important to re-process to get a more correct median. However, if you have 4 million data points, you won't see a significant difference after reprocessing and I wouldn't bother. Of course, most likely your number of data values is somewhere in between my two end case examples. As mentioned in the quote from my last comment, they say that averaging the two middle values is only worthwhile if you have less than 100 data points. If you have more, simply choosing the higher of the two middle values is largely sufficient.