chemia: Weighted arithmetic mean

Evidence: 100 • authority: 72

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

Evidence: 47 • authority: 92

A Beginner's Guide to the Annex E Scoring System of ISO 10993-6.. ISO 10993-6 provides the normative framework for assessing local tissue effects after implantation of medical device materials and is widely used in preclinical biological evaluation. Despite its broad application, the standard is frequently misunderstood in both teaching and practice, particularly regarding the logic of its semi-quantitative scoring system. This article aims to clarify the role of ISO 10993-6 within the broader ISO 10993 series, to correct a common misconception about the Annex E calculation, and to distinguish normative requirements from regulatory expectations and laboratory best practice. The Annex E irri…

Evidence: 43 • authority: 88

Median as a Weighted Arithmetic Mean of All Sample Observations. Median, a well known measure of central tendency, of a sample data x =(x1, x2, ... ,xn) is obtained through the traditional method as (xn-m + xm+1)/2, where m= int(n/2) and values of x are arranged in ascending (descending) order. Since, for odd n, n-m=m+1, the formula uses only one value from the sample data. For even n, only two middlemost values are used. This property of the formula invites the popular criticism of median being not based on all sample observations. It is possible to use an alternative formula to compute median as a weighted arithmetic mean of all sample observations, where weights are non-trivial and itera…

Evidence: 43 • authority: 72

In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as times of day, and fractional parts of real numbers. This is necessary since most of the usual means may not be appropriate on angle-like quantities. For example, the arithmetic mean of 0° and 360° is 180°, which is misleading because 360° equals 0° modulo a full cycle. As another example, the "average time" between 11 PM and 1 AM is either midnight or noon, depending on whether the two times are part of a single night or part of a single calendar day. The circular mean is one of the simplest examples of directional statistics and of statistics of non-Euclidean…

Evidence: 37 • authority: 80

Impulsive Noise Removal with an Adaptive Weighted Arithmetic Mean Operator for Any Noise Density

Evidence: 37 • authority: 92

Aggregation processes in customer rating systems - Insights from an economic decision experiment.. The aggregation of rating metrics in reputation systems is crucial for mitigating information overload by condensing customer rating distributions into singular valence scores. While platforms typically employ technical aggregation functions, such as the arithmetic mean to capture product quality, it remains unclear whether these functions align with customers' innate aggregation patterns. To address this knowledge gap, we designed a controlled economic decision experiment to elicit customers' aggregation principles by analyzing their product ranking decisions and contrasting these with variou…

Evidence: 37 • authority: 92

Comparison of Sizing Methods to Optimize Device Selection for Percutaneous Closure of Atrial Septal Defects.. Background and aims Accurate sizing of atrial septal defects (ASDs) is crucial for appropriate device selection during percutaneous transcatheter closure. Despite the availability of multiple imaging and sizing techniques, no consensus exists on the optimal method for determining device size. This study aimed to compare preprocedural ASD measurements obtained using different techniques with the final device waist diameter and to identify the measurement method demonstrating the most favorable agreement and reproducibility. Methods This retrospective study included 149 pediatric pati…

Evidence: 35 • authority: 80

Figure 12: Mesh-weighted arithmetic mean (MWAM) von Mises stress values in each FE model.

Evidence: 35 • authority: 72

A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community). Diversity indices are statistical representations of different aspects of biodiversity (e.g. richness, evenness, and dominance), which are useful simplifications for comparing different communities or sites. When diversity indices are used in ecology, the types of interest are usually species, but they can also be other categories, such as genera, families, functional types, or haplotypes. The entities of interest are usually individual organisms (e.g. plants or animals), and the measure of abundance can be, for example, number of individuals, biomass or coverage. In…