[Solved] The math percentage paradox - Page 1
Forum section: electronics / general

author: ballsystemlord
author_rank: Frequent Contributor
timestamp: September 21, 2023, 02:49:20 am
content: There's knowing math, and then there's understanding math. Of course I strive for the latter, but there's one or two things that have always confused me. (I do know algebra.)Here's a real word example. 7 parts are $0.21, those same ones from another seller are $0.32 for the 6 and $0.39 for the seventh. I want to figure out the percentage difference between the two. There are two ways I can compute this...(0.21×7)×100)/(0.32×6+0.39) == 63.636%((0.32×6+0.39)×100)/(0.21×7) == 157.143%Now ~57% is different than ~63% and much different that ~36.4%, which would be 100% - %63.6.So which of the above is correct math?If both, why/how?I don't get it at all. 2 is 200% of 1. and 1 is 50% of 2. I don't doubt that. But 200% (or 100% greater), and 50% are both very different numbers. But there has to be a reason to compute it one way or the other, right?Thanks!

author: TimFox
author_rank: Super Contributor
timestamp: September 21, 2023, 03:31:40 am
content: I don't like percentages in this usage due to the following:If I increase a value by 20%, and then decrease it by 20%, I do not get back to the same place.However, if I increase a value by 5 dB, and then decrease it by 5 dB I do get back to the same place.When dealing with a client who disliked dB, we compromised by saying "increase by the ratio 1.2:1, then decrease by the ratio 1.2:1", which gets us back to the same place.(I prefer ratios greater than unity, inverting the ratio if needed.)

author: vad
author_rank: Frequent Contributor
timestamp: September 21, 2023, 03:36:55 am
content: If you are looking for linearity, consider using a logarithmic scale.The base 2 logarithm of 200% is 1. The base 2 logarithm of 50% is -1.The natural logarithm of 63.636% is approximately -0.45200. The natural logarithm of 157.143% is approximately 0.45200.

author: Sredni
author_rank: Frequent Contributor
timestamp: September 21, 2023, 04:42:44 am
content: And things gets even more interesting on graphs.Plot the function x / (1+x)^2 on a linear scale, and you get a very asymmetric function, with inflection points placed asymmetrically with respect to the peak.Plot in on semilog scale and the function becomes symmetric with respect to the peak, including the position of the inflection points.Plot in on a loglog scale and you get rid of the inflection points as well.

author: andy3055
author_rank: Super Contributor
timestamp: September 21, 2023, 05:49:54 am
content: If you go with the first vendor, you pay 7x0.21 in total which is 1.47.The second vendor charges (0.32x6)+0.39 or a total of 2.31. The difference is 0.84 or the second person charges you 0.84 more than the first person. So, the percentage you are overpaying (if you buy from the second vendor) is (0.84/1.47)x100, which is 57.14%

author: Shonky
author_rank: Frequent Contributor
timestamp: September 21, 2023, 06:06:04 am
content: To explain your variance without getting into logs etc.63.636% = 0.63636157.143% = 1.571431/0.63636 = 1.57143.

author: IanB
author_rank: Super Contributor
timestamp: September 21, 2023, 06:20:49 am
content: To understand, just do the calculation with simple numbers:100 is 25% more than 80.80 is 20% less than 100.Then look at the percentages as ratios:100 is 125% of 80.100 is 80 × 1.2580 is 100 ÷ 1.2580 is 80% of 100.80 is 100 × 0.8100 is 80 ÷ 0.8100 is 80 × 1.25100 is 80 ÷ 0.80.8 = 1 ÷ 1.251.25 = 1 ÷ 0.80.8 × 1.25 = 1All clear?

author: hans
author_rank: Super Contributor
timestamp: September 21, 2023, 06:52:24 am
content: Seller A= 7x0.21=1.47Seller B=0.32x6+0.39=2.31You could say seller A is 36.4% cheaper than seller B (1 - 1.47/2.31).Or seller B is 57.1% more expensive (2.31/1.47 - 1).But both express the same difference. As was shown here already; 1/157.1%=63.6%