The weighted mean and its improved dispersion
Journal of Physical Chemistry & Biophysics

Journal of Physical Chemistry & Biophysics
Open Access

ISSN: 2161-0398

+44 1467840001

The weighted mean and its improved dispersion

International Conference on Physics

June 27-29, 2016 New Orleans, USA

L E Grigorescu

Horia Hulubei National Institute of Physics and Nuclear Engineering, Romania

Posters & Accepted Abstracts: J Phys Chem Biophys

Abstract :

Statistics is involved in every physical measurement.The weighted mean appears when a physical quantity is measured by different methods in different laboratories, producing different results. The formula is: The formula is: (1) with -absolute weights and - relative weights. A relation exists: (2) with - the individual standard deviations. To , two different dispersions are associated, D1 (internal) and D2 (external). The ratio D2/D1 is: (3) In practice (D2/D1)>1. So D2 is the confident one. In principle should produce as great deviations , as the associated are great. For equal treatment of these deviations, relative deviations may be considered: (4) which express the deviations in units . The n values from (4) must have same near (equivalent) values.Their arithmetical mean tends to zero.Thus, as in the case of a unique , we may reach the minimum of the expression: (5) The annulation of the derivative for , gives: (6) and finally formulas (1) and (2) are obtained. This calculus accepts great even with systematic uncertainties.In practice the theoretical unknown values , are replaced in formulae (1), (2) by the experimental value , which fluctuate. A dispersion D3 is obtained, by error propagation, and added to D1, D2. First are calculates:

Biography :