How does the percentage increase or decrease count: why does it fall back?
The base for percentage increases and decreases will change, with a 50 per cent increase and a 50 per cent drop, resulting in losses rather than even.
The most prone to errors in calculating increases or decreases is the base figure. Both increases and decreases are relative to current values, and the base figure has changed, with the same percentage corresponding to absolute amounts. For example, when a commodity goes up 50 to 150% and falls to 50%, it falls to 75 instead of 100. The same percentage rises and falls, always below the starting point.
Standard formulae
- Growth rate = (New - Original) ÷ Original value x 100%
- The drop rate is also based on the original value as the denominator, not the new value
- Multiplication of consecutive changes: Final = original value x (1+10%) x (1-10%)
- The percentage that needs to be increased to get back to square one is higher than the percentage that fell earlier. That's right.
Such delusions are common in investment and discounts: after a 20 per cent drop in equities, a 25 per cent increase is required to return the capital. The concept of the base figure is understood, and it is possible to avoid being misled by the `average increase' when looking at the [average median number] (/mean-median-mode). The conversion of discounts to matching can be referred to [proportional versus matching] (/ratio-and-scaling). The day-to-day mind-to-heart skills are found in [percentage mind-to-heart] techniques (/mental-percentage-tricks).
What about the successive percentages?
Multiple changes do not simply add or decrease by percentage, but multiply each factor. For example, the increase of 10 per cent and the drop of 10 per cent in two years, respectively, resulted in a net drop of 1 per cent at the original value of 1.1 x 0.9 = 0.99. This is consistent with the logic of cumulative errors in [rounding-significant-figures] (/rounding-significant-figures), which can be easily added to the measurement.