Wed Feb 13, 2013, 04:02 PM
pokerfan (27,442 posts)
The math of online dating
An interesting Ted-Ed released today. Ted-Ed is trying to give RSA Animate a run for best online eductional animations.
When two people join a dating website, they are matched according to shared interests and how they answer a number of personal questions. But how do sites calculate the likelihood of a successful relationship? Christian Rudder, one of the founders of popular dating site OKCupid, details the algorithm behind 'hitting it off.' Lesson by Christian Rudder, animation by TED-Ed.
Geometric Meaning of the Geometric Mean
The geometric mean of two positive numbers a and b is the (positive) number g whose square equals the product ab:
g2 = ab.
Euclid VI.13 gives a geometric construction of the mean proportional: Draw a semicircle on a diameter of length a + b and a perpendicular to the diameter where the two segments join. The length of the perpendicular from the circumference to the diameter is exactly the geometric mean of a and b.
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The math of online dating (Original post)
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Response to pokerfan (Original post)
Thu Feb 14, 2013, 08:26 PM
Jim__ (10,215 posts)
5. Talking about the geometric mean ...
Wikipedia has a pretty good article on it. It talks a little about the geometric meaning, but more about why it is useful and gives some interesting examples. An excerpt:
A geometric mean is often used when comparing different items – finding a single "figure of merit" for these items – when each item has multiple properties that have different numeric ranges. For example, the geometric mean can give a meaningful "average" to compare two companies which are each rated at 0 to 5 for their environmental sustainability, and are rated at 0 to 100 for their financial viability. If an arithmetic mean was used instead of a geometric mean, the financial viability is given more weight because its numeric range is larger- so a small percentage change in the financial rating (e.g. going from 80 to 90) makes a much larger difference in the arithmetic mean than a large percentage change in environmental sustainability (e.g. going from 2 to 5). The use of a geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting, and a given percentage change in any of the properties has the same effect on the geometric mean. So, a 20% change in environmental sustainability from 4 to 4.8 has the same effect on the geometric mean as a 20% change in financial viability from 60 to 72.
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.
Suppose an orange tree yields 100 oranges one year and then 180, 210 and 300 the following years, so the growth is 80%, 16.6666% and 42.8571% for each year respectively. Using the arithmetic mean calculates a (linear) average growth of 46.5079% (80% + 16.6666% + 42.8571% divided by 3). However, if we start with 100 oranges and let it grow 46.5079% each year, the result is 314 oranges, not 300, so the linear average over-states the year-on-year growth.
Instead, we can use the geometric mean. Growing with 80% corresponds to multiplying with 1.80, so we take the geometric mean of 1.80, 1.166666 and 1.428571, i.e. (1.80 * 1.166666 * 1.428571)1/3= 1.442249; thus the "average" growth per year is 44.2249%. If we start with 100 oranges and let the number grow with 44.2249% each year, the result is 300 oranges.