A hairy man wants to get rid of all of his hair. He recently came up with a new technique to shake his head (three narrow circles followed by a rapid left-rgiht shaking), and he wants to test the long-term efficacy of this shake for removing hair. He thus proceeds as follows:
Preface: on each day, some hair regrows and some hair falls out.
On day 1 he performs his shake. Then he counts the number $h_1$ of hairs fallen to the gorund.
On day 2 he does nothing and he again counts the number of hairs $h_2$ on the ground.
On day 3 he performs a second shake, which results in $h_3$ hairs on the ground.
On day 4 he rests, resulting in $h_4$ fallen hairs.
On day 5 he takes some chemical, which removes about $90$% of the remaining hair. He counts $h_5$ fallen hairs.
What would be a meaningful quantity to estimate the efficacy of the shake, using only $h_1,...,h_5$? The most natural quantity would be $\frac{\text{number of hairs before day 1}}{\text{number of hairs after day 4}}$, but he can't count the hair on his head. Would $\frac{h_1+h_2+h_3+h_4}{h_1+h_2+h_3+h_4+h_5/0.9}$ do the job? Or $\frac{h_1+h_3}{h_1+h_3+h_5/0.9}$ Any ideas?