Solved – the interpretation of interquartile range

descriptive statistics

I have daily measurements of nitrogen dioxide for one year (365 days) and the interquartile (IQR) is 24 microgram per cubic meter. What does "24" mean in this context, apart from the definition of IQR which is the difference between the 25th and 75th percentile? How would you explain this figure to a journalist, for example?

Thanks

Best Answer

From definition, this defines the range witch holds 75-25=50 per cent of all measured values.

: (median-24/2,median+24/2). Median should be written somewhere near this IQR.
The above was false of course, it seems I was still sleeping when writing this; sorry for confusion. It is true that IQR is width of a range which holds 50% of data, but it is not centered in median -- one needs to know both Q1 and Q3 to localize this range.

In general IQR can be seen as a nonparametric (=when we don't assume that the distribution is Gaussian) equivalent to standard deviation -- both measure spread of the data. (Equivalent not equal, for SD, (mean-$\sigma$,mean+$\sigma$) holds 68.2% of perfectly normally distributed data).

EDIT: As for example, this is how it looks on normal data; red lines show $\pm 1\sigma$, the range showed by the box on box plot shows IQR, the histogram shows the data itself: alt text
you can see both show spread pretty good; $\pm 1\sigma$ range holds 68.3% of data (as expected). Now for non-normal data
alt text
the SD spread is widened due to long, asymmetric tail and $\pm 1\sigma$ holds 90.5% of data! (IQR holds 50% in both cases by definition)