Can I use several medians, IQRs, and N for each, to calculate the median and IQR for the composite group?

Question

I have measurements of a group divided into subsets, with a median, interquartile range (IQR), and total N for each subset.

I would like to calculate the median and IQR for the total group using this information. Is that possible?

Thanks!

Answer 1

No, it's not possible: there is not enough information. Means can be combined if the sizes of groups are known; medians and quartiles cannot be.

Example.

• the set $\{-1,0,1\}$ has median $0$; the set $\{2,3,4\}$ has median $3$. Their union has median $1.5$.
• the set $\{-5,0,5\}$ has median $0$; the set $\{2,3,4\}$ has median $3$. Their union has median $2.5$.

(Same story with IQR, but the examples would be more complicated).