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Basic Univariate Statistics
Published in Jhareswar Maiti, Multivariate Statistical Modeling in Engineering and Management, 2023
If we denote the first, second and third quartiles as Q1, Q2, and Q3, then the inter-quartile range (IQR) is Q3–Q1. But the measure that is widely used to define variability is standard deviation. Standard deviation is the square root of variance of a given data set where variance is the average squared deviation of the data points from their mean. Consider a sample of size n with mean x¯. The variance of the sample, denoted by s2, is computed using the following formula:s2=1n−1∑i=1n(xi−x¯)2
Quality Tools for Oil and Gas Industry
Published in Abdul Razzak Rumane, Quality Management in Oil and Gas Projects, 2021
Sigma is a Greek letter σ that stands for standard deviation. Standard deviation is a statistical way to describe how much variation exists in a set of data, a group of items, or a process. Standard deviation is the most useful measure of dispersion. Six Sigma means that a process to be capable at Six Sigma level, and the specification limits should be at least 6 σ from the average point. So the total spread between upper specification (control) limit and lower specification (control) limit should be 12 σ. With Motorola’s Six Sigma program, no more than 3.4 defects per million fall outside specification limits with process shift of not more than 1.5 σ from the average or mean. Six Sigma started as a defect reduction effort in manufacturing and was then applied to other business processes for the same purpose.
Distribution
Published in Frank R. Spellman, Fundamentals of Wastewater-Based Epidemiology, 2021
The standard deviation, s or σ (sigma), is often used as an indicator of precision. The standard deviation is a measure of the variation (the spread in a set of observations) in the results; that is, it gives us some idea whether most of the individuals in a population are close to the mean or spread out. In order to gain better understanding and perspective of the benefits derived from using statistical methods in epidemiology, it is appropriate to consider some of the basic theories of statistics. In any set of data, the true value (mean) will lie in the middle of all the measurements taken. This is true, provided the sample size is large and only random error is present in the analysis. In addition, the measurements will show a normal distribution as shown in Figure 5.1.
Performance Evaluation Towards Automatic Building and Road Detection Technique for High-Resolution Remote Sensing Images
Published in IETE Journal of Research, 2023
The IGV is computed by first computing the average gray value within the window w × w (w = 5). This is the sum of the gray values of all the pixels in the window divided by the number of pixels. The average gray value for each pixel (x, y) in the enhanced image (h) within the window can be calculated as Then, the candidate pixel value is generated by computing the standard deviation which is the difference between the gray values of each pixel in the enhanced image (h) to the average gray value. The standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Compute the IGV at (x, y) within the window as The sum of deviations at the boundary of man-made objects is significantly more than that of points inside the man-made objects. In contrast, the sums of deviations at the boundary of non-man made (natural) objects are not as high as man-made objects.
Predicting loads and dynamic responses of an offshore wind turbine in a nonlinear mixed sea
Published in Ships and Offshore Structures, 2021
We can notice from Figure 5 that the three wave time series have approximately the same mean value. However, the standard deviation values of the red curve and green curve wave time series in Figure 5 are quite different. In statistics, the standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. The standard deviation values in Table 2 quantitatively show that in Figure 5 the red curve from the nonlinear simulation with bottom effects fits perfectly with the blue curve from the transformed linear simulation with bottom effects. These standard deviation values in Table 2 also show quantitatively that in Figure 5 the two curves from nonlinear simulations with and without bottom effects deviate quite substantially from each other.
Reduction of Training Data Using Parallel Hyperplane for Support Vector Machine
Published in Applied Artificial Intelligence, 2019
Pardis Birzhandi, Kyung Tae Kim, Byungjun Lee, Hee Yong Youn
Here μ and σ are the mean and standard deviation of the normal distribution, and λ is the rate parameter of the exponential distribution. A low standard deviation indicates that the data points lie close to the mean of the data of the set, while a large value implies widespread. Therefore, standard deviation is an important parameter deciding the distribution of the distances between each pair of data points in a cluster. The effect of increasing the standard deviation on the normal distribution of the data points is illustrated in Figure 4. The upper set is distributed with μ = (4, 4) and σ = 0.8, while the lower set with μ = (−4, −4) and σ = 2. The figure shows that the distance between the data points grows by increasing the value of σ. The distance factor also affects the result of k-mean clustering algorithm. Consequently, the effectiveness of the PH scheme is affected by the value of standard deviation.