Math CentralQuandaries & Queries


Question from shahrukh:


We had a web page that was taking 12 secs to load. Now it loads in 3 secs.

What is the percentage of improvement or how much faster is it working now.

TO me it looks like it is working 3 times faster or there is a 300% improvement in the loading time.

However my client says its ((12-3)/12*)100 = 75% improved. Which seems illogical on the face of it.

Thanks for your help

I am always uncomfortable using percentages in your situation. Why not just say that it takes one-fourth the time? That sounds pretty impressive to me.
But, to answer your question, compare your situation to running a race -- a one-second improvement in the 100m dash is far more impressive than a 1-second improvement in the 1500m run. In the first case, going from, say, 10 seconds to 9 seconds represents an improvement of 1 second in 10, or 10%. In the second case, going from 200 seconds to 199 seconds represents an improvement of 1 second in 200, or .5% The rule for using percents is that YOU MUST HAVE A PERCENT OF SOMETHING. In my example, it is a percentage of the former record:
Improvement for the dash = 10% of 10 seconds = (.1)*10 = 1 second.
Improvement for the run = .5% of 200 seconds = (.005)*200 = 1 second.

Back to your example, sorry, but I agree with your client -- the improvement of 9 seconds is 75% of the former time of 12 seconds. An improvement of 100% would mean that the new procedure is instantaneous. You cannot do better than 100% of some quantity. (Athletes, no matter how determined, cannot give more than 100% of what they are capable of giving, despite what they might say in interviews.) The trouble with your claim is that there is no number available to multiply by 3 to end up with 3 seconds.



It is working 300% faster and the time is 75% shorter. With comparisons like this it is always important to specify exactly what quantity is changing! (Note also that if you changed back, it is the the speed that would reduce by 75% and the loading time that would increase by 300% !)

Good Hunting!

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