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In statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators. [1] [2] Indices – also known as indexes and composite indicators – summarize and rank specific observations. [2]
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
In 2019 if a market basket price is 55 and the basket were to double the following year, in 2020, then the index would rise to 200. This is done by performing a simple calculation: Dividing the new year market basket price by the reference year's (otherwise known as the base year) price, and subsequently multiplying the quotient by 100.
The automated readability index (ARI) is a readability test for English texts, designed to gauge the understandability of a text. Like the Flesch–Kincaid grade level, Gunning fog index , SMOG index , Fry readability formula , and Coleman–Liau index , it produces an approximate representation of the US grade level needed to comprehend the text.
Some representative refractive indices; Name of material λ (nm) Refractive index no. n Reference Vacuum: 1 (by definition) Air at STP: 1.000273 [citation needed] Gases at 0 °C and 1 atm Air: 589.29: 1.000293 [1] Carbon dioxide: 589.29: 1.00045 [2] [3] [4] Helium: 589.29: 1.000036 [1] Hydrogen: 589.29: 1.000132 [1] Liquids at 20 °C Arsenic ...
The Simpson index was introduced in 1949 by Edward H. Simpson to measure the degree of concentration when individuals are classified into types. [10] The same index was rediscovered by Orris C. Herfindahl in 1950. [11] The square root of the index had already been introduced in 1945 by the economist Albert O. Hirschman. [12]
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
When the quadratic mean diameter equals 10 inches (250 mm), the log of N equals the log of the stand density index. In equation form: log 10 SDI = -1.605(1) + k Which means that: k = log 10 SDI + 1.605 Substituting the value of k above into the reference-curve formula gives the equation: log 10 N = log 10 SDI + 1.605 - 1.605 log 10 D