• Arrows theorm
• Average, Medum, Mode
• Improper arguments
• Moral Politics
• Zip's law

• Arrows theorm

• Average, Medum, Mode see:

Average most often refers to the arithmetic mean, but is actually ambiguous
and may be used to also refer to the mode, median, or midrange.

The Arithmetic Mean (Usual definition of Average) is obtained by summing all elements of the data set and dividing by the number of elements. = $61.702.00

The Mode is the data element which occurs most frequently. = $61.190

The Median is the middle element when the data set is arranged in order of magnitude. =$25.000

e.g. see income tax results (2001)

Income range	Num. Returns	Total Income K$	Ave Income	Cum Returns	% Cum Returns
$1-to-$5,000	12592044	33298375	2,644.40	14030231	11%
$5,000-to-$10,000	12354102	92515491	7,488.65	26384333	20%
$10,000-to-$15,000	11903188	148650322	12,488.28	38287521	29%
$15,000-to-$20,000	11476963	200294955	17,451.91	49764484	38%
$20,000-to-$25,000	9971372	223549607	22,419.14	59735856	45%
$25,000-to-$30,000	8563035	235155806	27,461.74	68298891	52%
$30,000-to-$40,000	13843640	480541398	34,712.07	82142531	63%
$40,000-to-$50,000	10612617	475360387	44,792.00	92755148	71%
$50,000-to-$75,000	17559778	1074476035	61,189.61	110314926	85%
$75,000-to-$100,000	8903894	764115039	85,818.07	119218820	91%
$100,000-to-$200,000	8469199	1114318617	131,573.08	127688019	98%
$200,000-to-$500,000	2018372	578592628	286,663.03	129706391	99.6%
$500,000-to-$1,000,000	355617	240863950	677,312.81	130062008	99.8%
$1,000,000-to-$1,500,000	85479	103192473	1,207,226.02	130147487	99.917%
$1,500,000-to-$2,000,000	36491	62634095	1,716,425.83	130183978	99.945%
$2,000,000-to-$5,000,000	52157	154967884	2,971,180.93	130236135	99.985%
$5,000,000-to-$10,000,000	12266	83519500	6,809,024.95	130248401	99.995%
$10,000,000-or- more	6836	174988989	25,598,155.21	130255237	100%

 

• Improper arguments ( See: Misleading a Nervous America to the Wrong Conclusion )

1. false dilemma. This is when only two choices are given when, in reality, there are more options.
2. argument from ignorance. This involves claiming that what hasn’t been disproven must be true.
3. slippery slope. An argument portraying a series of increasingly bad events
4. ad hominem attack.Criticizing a person or group instead of an issue
5. appeal to authority. Arguing a claim is true based on someone being an expert on the subject

• Moral Politics

• Zip's law

Zipf's law, named after the Harvard linguistic professor George Kingsley Zipf (1902-1950), is the observation that frequency of occurrence of some event ( P ), as a function of the rank ( i) when the rank is determined by the above frequency of occurrence, is a power-law function Pi ~ 1/ia with the exponent a close to unity.

Note: This means that the Log Log plot of Frequency to Rank is linear:

• The most famous example of Zipf's law is the frequency of English words.
• The second example Zipf showed in his book was the population of cities (or population of communities)
• The income or revenue of a company as a function of the rank is also an example of the Zipf's law
• The economist Vilfredo Pareto observed that wealth follows a "predictable imbalance", with 20% of the population holding 80% of the wealth.
• Jacob Nielsen observed power law distributions in web site page views, (Frequently linked Blogs)