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In order to calculate the average and standard deviation from aggregate data, it is necessary to have available for each group: the total of values (Σx i = SUM(x)), the number of values (N=COUNT(x)) and the total of squares of the values (Σx i 2 =SUM(x 2)) of each groups.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
Excel pivot tables include the feature to directly query an online analytical processing (OLAP) server for retrieving data instead of getting the data from an Excel spreadsheet. On this configuration, a pivot table is a simple client of an OLAP server.
In mathematics, the Bernoulli numbers B n are a sequence of rational numbers which occur frequently in analysis.The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain ...
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Numbers is a spreadsheet application developed by Apple Inc. as part of the iWork productivity suite alongside Keynote and Pages. [2] Numbers is available for iOS and macOS High Sierra or newer. [3] Numbers 1.0 on Mac OS X was announced on August 7, 2007, making it the newest application in the iWork suite.
The use of exponential generating functions (EGFs) to study the properties of Stirling numbers is a classical exercise in combinatorial mathematics and possibly the canonical example of how symbolic combinatorics is used. It also illustrates the parallels in the construction of these two types of numbers, lending support to the binomial-style ...
"In recent weeks I have spoken to a large number of former and current Yankees -- spanning several eras -- to elicit their perspectives on our longstanding facial hair and grooming policy, and I ...