Shape-based averaging

Torsten Rohlfing1, Calvin R Maurer

  • 1SRI International, Menlo Park, CA 94025-3493, USA. torsten@synapse.sri.com

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Shape and Texture of Coarse Aggregate01:25

Shape and Texture of Coarse Aggregate

Aggregate shape is classified based on the relative sharpness or roundness of the edges and corners. This classification includes categories like rounded, angular, elongated, and flaky, each with specific characteristics. Rounded aggregates, fully shaped by attrition, are typical of river or seashore gravel, while angular aggregates, such as crushed rock, have well-defined edges. Aggregates that are elongated and flaky are less desirable, as they can reduce the workability and strength of...
Average Value on a Rectangle01:27

Average Value on a Rectangle

A snowfall map can represent how snow depth varies across a region, such as Colorado, over a fixed time period. Since different locations may receive different amounts of snow, the snowfall depth is described by a function of two variables. If f(x,y) represents the snow depth at a point in a rectangular region, then the average snowfall over the entire region is found by comparing the total accumulated snowfall with the area being measured.Total Snowfall over a RegionThe total snowfall over a...
Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
Trimmed Mean01:10

Trimmed Mean

While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...
Design Example: Aggregate Gradation01:24

Design Example: Aggregate Gradation

The right type and quality of aggregates are crucial for concrete as they significantly influence its properties, mix proportions, and cost-effectiveness. If different sources are available for sand, the commonly used fine aggregate in concrete, the selection of sand is primarily based on its gradation.
The grading, or particle-size distribution, of sand is determined using sieve analysis, with standard sizes ranging from 150 μm to 10 mm (ASTM No. 100 sieve to 3⁄8 in. sieve). Sand is sampled...
Geometric Mean01:15

Geometric Mean

The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...