A finding from Qubix University
Up 50%, then down 50%, leaves you 25% down
A price that rises by half and then falls by half does not come back. It ends a quarter below where it started.
| February | £100 | |
|---|---|---|
| March, up 50% | £150 | +£50 |
| April, down 50% | £75 | −£75 |
| Against February | −25% | not level |
The two percentages look like opposites and are not, because they are percentages of different numbers.
The rise is half of the starting price. The fall is half of the raised price, which is a bigger number, so it takes away more than the rise added.
This is why a percentage on its own says almost nothing. The figure you need beside it is what it was a percentage of.
Arithmetic: 100 × 1.5 = 150, and 150 × 0.5 = 75.
Taught in Chapter 2 · Absolute change, relative change and rate of change.
Qubix University is a data-science course being written in the open. Volume 0 is a draft: it has not been through final review, and nothing in it is accredited. The finding above is arithmetic, and stands on its own.