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index
An alphabetically ordered list of keywords, names, or topics at the end of a book that indicates on which pages they can be found.
Wenn du das Kapitel nicht findest, schau im Index nach.
If you can't find the chapter, look it up in the index.
In connection with books or academic papers, 'der Index' (the index) always refers to the keyword index at the end. The typical verb in this context is 'nachschlagen' (to look up).
Ich habe den Begriff im Index des Fachbuchs nachgeschlagen.
I looked up the term in the index of the textbook.
In news about business and finance, 'Index' (index) means a figure that measures a trend or development. You often hear of an 'Aktienindex' (stock index) or 'Preisindex' (price index).
Der Index der Verbraucherpreise ist leicht gesunken.
The consumer price index has fallen slightly.
The fixed expression 'auf dem Index stehen' means that a medium (e.g. a film or video game) has been classified as harmful to minors and may only be sold with restrictions.
Dieses Computerspiel stand lange auf dem Index.
This computer game was on the restricted list for a long time.
In mathematics, computer science, or other sciences, an 'Index' (index) is a small number or letter that indicates the position of an element in a series.
In der Formel steht der Index „i“ für eine beliebige ganze Zahl von 1 bis 10.
In the formula, the index 'i' stands for any whole number from 1 to 10.
average / cross-section
'der Durchschnitt' and 'der Index' can both appear in statistics, economics, or numerical comparisons. 'Durchschnitt' means an average: you add several values together and divide them by their number. 'Index' is a figure that shows how a group of values changes, for example prices or stock prices. The words can be confusing because an index is often calculated from many values. But an average is more about 'how high is the middle value?', while an index is more about 'how has something changed in comparison?'.
Der Index zeigt, dass die Preise in diesem Jahr deutlich gestiegen sind.
The index shows that prices have risen significantly this year.
Der Durchschnitt der Testergebnisse liegt in dieser Klasse bei 78 Punkten.
The average test score in this class is 78 points.