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In particular, for octahedral $X$ and $Y$ and for $p$ in $(1,\\infty)$ the space $X\\oplus_p Y$ is $2^{1-1/p}$-average rough, which is in general optimal. Another consequence is that for any $\\delta$ in $(1,2]$ there is a Banach space which is exactly $\\delta$-average rough. We give a complete characterization when an absolute sum of two Banach spaces is octahedral or has the strong diameter 2 property. 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