A set of 12 readings has mean 34 and median 31. Every reading is multiplied by 5 and then 12 is subtracted from each result. What are the mean and the median of the new readings?

A change of the form $y=5x-12$ multiplies by a positive number and then shifts, so it keeps the readings in the same order. The mean follows the rule directly: $5\times 34-12=158$. The middle reading is still the middle reading afterwards, so the median follows the same rule: $5\times 31-12=143$. Stopping at the multiplication gives 170 and 155; treating the median as untouched keeps it at 31, which is true for a reordering but not for a rescaling; and subtracting before multiplying gives $5(34-12)=110$ and $5(31-12)=95$, a different transformation altogether.