how Matlab iqr works

According to this wiki link (https://en.wikipedia.org/wiki/Interquartile_range), the iqr for this set of data

     102   104   105   107   108   109   110   112   115   116   118

should be 115 - 105 = 10. I wonder why Matlab give me value of 8.75.

[Dajiang]

I just came across this web page ( http://math.stackexchange.com/questions/65391/calculating-interquartile-range ). It seems several ways to calculate iqr(x); all of which will output similar result, I guess, if length(x) is big enough. Isn't it? However, I wonder how Matlab implements it.

Answer 1

[Steven Lord]

If you're using the Statistics and Machine Learning Toolbox IQR function, the description of the output argument described what it does. The definition of Q1 and Q3 from that Wikipedia page are different from the definition given in the QUANTILE function. The quantile values for the vector do not necessarily need to be in the vector. They may be, if the length of the vector allows for it or if there are repeated values, but they are not required to be. This difference explains the different results.

Answer 2

[Brendan Hamm]

MATLAB uses the prctile() function to find Q3 and Q1 to calculate the IQR. See Quantiles and Percentiles for descriptions on how this calculation is performed.