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Research Methods
Published in Nancy J. Stone, Chaparro Alex, Joseph R. Keebler, Barbara S. Chaparro, Daniel S. McConnell, Introduction to Human Factors, 2017
Nancy J. Stone, Chaparro Alex, Joseph R. Keebler, Barbara S. Chaparro, Daniel S. McConnell
Besides the frequency distribution, we can calculate the “average” or central tendency. We measure central tendency in three ways: the mean, the median, and the mode. The mean is the arithmetic average. If five individuals responded to a survey item using a scale from 1 to 5 (very satisfied to very dissatisfied) and the responses were 1, 2, 3, 4, and 5, then the mean would equal the sum of all responses divided by 5, the number of respondents. In this case, the mean would be (1 + 2 + 3 + 4 + 5)/5 = 3. The median is the mid point of the distribution. If your data set included the following responses: 4, 3, 4, 5, 2, 4, 4, 1, 5, 6, 7, a frequency distribution table can often help you “see” the median (see Table 2.3). In this example, the median would be 3 because this splits your distribution in half—there are four values below and four values above the 3. Finally, the mode is the most frequently occurring number. From Table 2.3 we see that there are five threes, which are easier to see when plotted in a histogram, as shown in see Figure 2.7. Therefore, the mode also would be 3. It is possible to have more than one mode in a data set. Sometimes the data sets are bi modal where there are two modes, tri modal, which includes three modes, or multi modal, where there are more than three modes.
Probability Distributions of Univariate Data
Published in Nong Ye, Data Mining, 2013
The mode of a probability distribution for a variable x is located at the value of x that has the maximum probability density. When a probability density function has multiple local maxima, the probability distribution has multiple modes. A large probability density indicates a cluster of similar data points. Hence, the mode is related to the clustering of data points. A normal distribution and a skewed distribution are examples of unimodal distributions with only one mode, in contrast to multimodal distributions with multiple modes. A uniform distribution has no significant mode since data are evenly distributed and are not formed into clusters. The dip test (Hartigan and Hartigan, 1985) determines whether or not a probability distribution is unimodal. The mode test in the R statistical software (www.r-project.org) determines the significance of each potential mode in a probability distribution and gives the number of significant modes.
Fundamentals of Multiphase Flow
Published in Efstathios E. Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Multiphase Flow Handbook, 2016
Efstathios E. Michaelides, Zhi-Gang Feng
e mode is the size that corresponds to the maximum of a continuous frequency function. A distribution that has two local maxima is referred to as a bimodal distribution and it has two modes. Similarly, trimodal and multimodal distributions may be de ned, but they are seldom met in dispersed multiphase ows. e corresponding mode for a discrete size distribution is the size that corresponds to the highest value in the frequency histogram. For example, d5 is the mode of the discrete distribution depicted in Figure 1.3.
Preventing stress singularities in peri-implant bone – a finite element analysis using a graded bone model
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Oliver Roffmann, Meike Stiesch, Andreas Greuling
The next step was to choose a value for the transition zone used in this study from all of this measured points. For this purpose, the mode was calculated from the measured data. The mode is the value that occurs most frequently in data set and is more insensitive to measurement errors or artefacts then the mean value. As the data is continuous, a kernel density estimation approach was chosen to calculate the mode. In this study the Matlab function ksdensity was incorporated in the automation script to return a probability density estimate with an automatically chosen bandwidth of 0.2189. The mode of the density function delivers a value of and was chosen as the width for the transition zone. In order to calculate the cortical width of the graded approach, the thick cortical layer of the conventional approach served as the starting point. It was assumed, that half of the transition zone covers the former cortical region. This resulted in a thickness of the cortical layer of
Introducing novel statistical-based method of screening and combining currently well-known surrogate safety measures
Published in Transportation Letters, 2022
Navid Nadimi, Amir Mohammadian Amiri, Amirhossein Sadri
Where k is the number of solutions of the Equation (7).3-The relative frequency for the most critical value of an SSM must be zero. In other words, the last point in the distribution function must be on the horizontal axis.Where Xt is the most critical value of the SSM.4-In the distribution function, the mode must be before the third quartile (Q3). The mode is the most frequent value. When a SSM is going to the critical values, it is expected that the frequency curve being decreasing. If the mode is after the Q3, then despite being in the critical range of the SSM, we have the most frequency. Therefore, this is not a proper SSM for safety evaluations.
Different Power Adaptive Transmission Schemes Over Alternate Rician Shadowed Fading Channels
Published in IETE Journal of Research, 2023
Laishram Mona Devi, Aheibam Dinamani Singh
Random fluctuation of received signals and shadowing phenomena are among the major factors contributing to the degradation of channel quality in wireless communication [1]. New fading models that can more closely resemble the behaviors of real physical fading channels have been proposed by various researchers. Recently, Alternate Rician shadowed (ARS) fading channels were introduced in [2]. The ARS fading model consists of two fluctuating specular components in which only one is active at a particular time [2]. This model can provide left or right-sided bimodality. The term bimodal is a continuous probability distribution having two different modes. It makes this model fitter for body-centric communication because of bimodal fading distribution [3,4]. Such fading distribution is produced due to rotation of the body, spinning of arms, etc. In body-centric communication, the system transducer which attaches to the body acts either as a relay or final node to the network of device-to-device communication [5]. Different regions of the human body cause shadowing in the transmitted signals. This type of phenomenon is known as body shadowing. It occurs when one or more human body parts obstruct the path of the broadcasted signal [6]. Classical fading models such as Rician, Nakagami, Hoyt, etc., are all unimodal. They do not fit body-centric communication scenarios [6]. The two-wave with diffuse power (TWDP) and fluctuating two-ray (FTR) channels, on the other hand, are bimodal fading models. And yet, they exhibit only one-sided bimodality in the experimental works of [7–10]. Therefore, for body-centric communication, ARS fading channels are an appropriate choice of fading model.