Index

An index is an indirect shortcut derived from and pointing into a greater volume of values, data, information or knowledge. Index may refer to:

Business

Publishing

Index (statistics)

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. Indexes summarize and rank specific observations.

Much data in the field of social sciences is represented in various indices such as Gender Gap Index, Human Development Index or the Dow Jones Industrial Average.

Item in indexes are usually weighted equally, unless there are some reasons against it (for example, if two items reflect essentially the same aspect of a variable, they could have a weight of 0.5 each).

Constructing the items involves four steps. First, items should be selected based on their face validity, unidimensionality, the degree of specificity in which a dimension is to be measured, and their amount of variance. Items should be empirically related to one another, which leads to the second step of examining their multivariate relationships. Third, indexes scores are designed, which involves determining their score ranges and weights for the items. Finally, indexes should be validateds, which involves testing whether they can predict indicators related to the measured variable not used in their construction.

Index of a subgroup

In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively "half" of the elements of G lie in H. The index of H in G is usually denoted |G : H| or [G : H] or (G:H).

Formally, the index of H in G is defined as the number of cosets of H in G. (The number of left cosets of H in G is always equal to the number of right cosets.) For example, let Z be the group of integers under addition, and let 2Z be the subgroup of Z consisting of the even integers. Then 2Z has two cosets in Z (namely the even integers and the odd integers), so the index of 2Z in Z is two. To generalize,

for any positive integer n.

If N is a normal subgroup of G, then the index of N in G is also equal to the order of the quotient group G / N, since this is defined in terms of a group structure on the set of cosets of N in G.

If G is infinite, the index of a subgroup H will in general be a non-zero cardinal number. It may be finite - that is, a positive integer - as the example above shows.

Inside (Ronnie Milsap album)

Inside is the fourteenth studio album by Ronnie Milsap. It was released in 1982 under the RCA Records Label. It contains the hits "Any Day Now", "Inside", and "He Got You".

Track listing

Production

Personnel

Outside (jazz)

In jazz improvisation, outside playing, describes an approach where one plays over a scale, mode or chord that is harmonically distant from the given chord. There are several common techniques to playing outside, that include side-stepping or side-slipping, superimposition of Coltrane changes, and polytonality.

Side-slipping

The term side-slipping or side-stepping has been used to describe several similar yet distinct methods of playing outside. In one version, one plays only the five "'wrong'" non-scale notes for the given chord and none of the seven scale or three to four chord tones, given that there are twelve notes in the equal tempered scale and heptatonic scales are generally used. Another technique described as sideslipping is the addition of distant ii-V relationships, such as a half-step above the original ii-V. This increases chromatic tension as it first moves away and then towards the tonic. Lastly, side-slipping can be described as playing in a scale a half-step above or below a given chord, before resolving, creating tension and release.

Inside (David Sanborn album)

Inside is a studio album by David Sanborn, released through Elektra Records in 1999. In 2000, the album won Sanborn the Grammy Award for Best Contemporary Jazz Performance.

References