Accession Number : AD0910312

Title :   Geometric-vs-Arithmetic Averaging of Positive Random Variables.

Descriptive Note : Technical rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEWPORT RI

Personal Author(s) : Schmidlin, Dean J.

Report Date : 03 MAY 1973

Pagination or Media Count : 24

Abstract : Many comparisons have shown that when acoustic data are analyzed by different processing systems, there are significant variations in the calculated values of sound pressure levels. Since the Naval Underwater Systems Center is engaged in making reliable underwater radiated noise measurements, the Center is interested in quantitative as well as qualitative explanations for these differences. The variations are due in part to the diverse methods used for data averaging. This report is the first of a series of reports dealing with the averaging of discrete and continuous data. In this report, the geometric mean is defined for a positive random variable, and methods are derived for computing the geometric mean. A quantity R is also defined which expresses the relative difference between geometric and arithmetic averaging. Examples are then presented to illustrate the application of the derived methods, and to indicate the difference between the geometric and arithmetic averages of several well-known probability distributions. (Author)

Descriptors :   (*RANDOM VARIABLES, STATISTICAL ANALYSIS), SOUND, MEASUREMENT, PRESSURE, STATISTICAL DATA, ACCURACY, RELIABILITY, PROBABILITY, STANDARDS, MILITARY REQUIREMENTS, NOISE, UNDERWATER SOUND, DETERMINATION, INSTRUCTION MANUALS.

Subject Categories : Statistics and Probability
      Acoustics

Distribution Statement : APPROVED FOR PUBLIC RELEASE