What would the correct English description be for the difference for 1/3

Question

If you measure a task & it takes 3 seconds, then the next time you do the same task, it takes you 1 second, is the difference 200% or 67%?

Or would you say the difference is 200% because 3-1=2 or 200% better -- but the percentage of difference is 2/3 or 67%? I'm pretty sure I'm confusing something if not someone. Be that as it may, I need to explain this clearly so that the analysis is clear & credible. The example I would site would be: Let's say you are mesuring system transaction response times & on two separate tests find the response time improvement noted. (Thanks PH)

It was done in one third the time or three times the speed. – JTP - Apologise to Monica Mar 31 '15 at 00:14 — JTP - Apologise to Monica, Mar 31 '15 at 00:14

score 0 · Answer 1 · answered Mar 31 '15 at 00:08

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I would assume you are doing 300% better because you could perform the task 3 times in the same amount of time

answered Mar 31 '15 at 00:08

user2973447

581

2

300% as well, but 200% better. If your time had no change at all, would you say 100% better? – JTP - Apologise to Monica Mar 31 '15 at 00:14

score 0 · Answer 2 · answered Mar 31 '15 at 00:19

For maximum clarity, I would simply say "The time per task improved from three seconds to one second". If you desire to use percentages, percentage change is expressed as $\frac{\text{new}-\text{old}}{\text{old}}$. So you could say "The time per task decreased $66\frac{2}{3}\%$, from 3 seconds to 1".

Assuming the task is being performed continuously, you could instead measure tasks completed per unit time, which has improved from $\frac{\text{time}}{3}$ to $\frac{\text{time}}{1}$, a $\frac{\text{time}-\text{time}/3}{\text{time}/3}=\frac{2(\text{time})/3}{\text{time}/3}=2=200\%$ improvement.

So both are correct, but it depends on how exactly you measure "improvement".

What would the correct English description be for the difference for 1/3

2 Answers2