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In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
Representation of the three-sigma rule. The dark blue zone represents observations within one standard deviation (σ) to either side of the mean (μ), which accounts for about 68.3% of the population. Two standard deviations from the mean (dark and medium blue) account for about 95.4%, and three standard deviations (dark, medium, and light blue ...
The approximate value of this number is 1.96, meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean. Because of the central limit theorem, this number is used in the construction of approximate 95% confidence intervals. Its ubiquity is due to the arbitrary but common convention of using ...
as for "three sigma rule", idk, this sounds as if it was a rule dealing with a 3-sigma case, while "68-95-99.7" is actually a list of cases of n sigma, with a modest n=1..3. The page title actually helped me remember "68-95-99.7" by now, but as 4 or 5 sigma also occur in everyday considerations, I keep having to look it up anyway.
Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions. Chebyshev's inequality is more general, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 88.89% within three standard deviations for a broad range of different probability distributions. [1] [2]
Of the total Muslim population, 87–90% are Sunni and 10–13% are Shi'a. Most Shi'as (between 68% and 80%) live in mainly four countries: Iran, Azerbaijan, Bahrain, and Iraq. [31] Furthermore, there are concentrated Shi'a populations in Lebanon, Russia, China, Pakistan, Bangladesh and 10 sub-Saharan African countries. [32]
The main combat and combat support units are 68 armoured regiments, and over 350 infantry battalions and 300 artillery regiments (including two surface-to-surface missile (SSM) units). Among major armaments and equipment, there are 4,614 main battle tanks, more than 150,000 vehicles, 140 self-propelled artillery, 3,243 towed artillery, more ...
Secunderabad had an average literacy rate of 73%, male literacy was 78%, and female literacy was 68%. 11% of the population was under 6 years of age. The city has a sizable population of Anglo-Indians , who mainly resided in the South Lallaguda area of Secunderabad which was popularly known as Little England. [ 27 ]