Where x is a measurement, is the mean, and f(x) is the ordinate of the distributionĬurve for that value of x. The distributions encountered in physics often have a mathematical shape given Or, simply the square root of the mean squareĥ.4 DISPERSION MEASURES APPROPRIATE TO GAUSSIAN DISTRIBUTIONS ROOT MEAN SQUARE DEVIATION The square root of the average of the The average of the sum of the squares of the (usually justĪVERAGE DEVIATION, abbreviated lower case, a. Some commonly used measures of dispersion are listed forĪVERAGE DEVIATION FROM THE MEAN. The difference between a measurement and the mean of its distribution is called theĭEVIATION (or VARIATION) of that measurement. The value at which the peak of the distribution curve occurs.) MODE The most frequent value in a set of measurements. The middle value of a set of measurements ranked in numerical The reciprocal of the average of the reciprocals of The nth root of the product of n positive Of the measurements divided by the number of measurements. (or simply the MEAN, or the AVERAGE): The sum
Some of the "measures of central tendency" commonly used are listed here forĪRITHMETIC MEAN. The mathematicalĭiscipline of statistics has developed systematic ways to do this. We canĭescribe the measurement and its uncertainty by just a few numbers. The distribution curves by measures of dispersion (spread), skewness, etc. One value (some kind of average), so also we can represent the shape of One can often guess the shape of the curve, even with a finite set of values, especially Such aĬurve is called an error distribution curve. The tops of the bars are connected with a smooth curve. Number of values is very large, and a bar graph (Fig. As always, one proceeds on the basis of reasonableĬonsider a large number of repeated measured values of a physical quantity. In practice, one must deal with a finite set of values, so the nature of their distribution Some of the methods for accurately describing the nature of measurement distributions. Intuitive way, without inquiring into the nature of the scatter.
Up to this point, the discussion has treated the "scatter" of measurements in an
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