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Presentation of statistical data
Published in John Bird, Basic Engineering Mathematics, 2017
A frequency distribution is merely a table showing classes and their corresponding frequencies (see Problems 8 and 12). The new set of values obtained by forming a frequency distribution is called grouped data. The terms used in connection with grouped data are shown in Fig. 32.6(a). The size or range of a class is given by the upper class boundary value minus the lower class boundary value and in Fig. 32.6(b) is 7.65-7.35; $ {7}.{65}\!-\!{7}.{35}; $ i.e. 0.30. The class interval for the class shown in Fig. 32.6(b) is 7.4 to 7.6 and the class mid-point value is given by (upper class boundary value)+(lower class boundary value)2 $$ \begin{aligned} \frac{(\text{ upper} \text{ class} \text{ boundary} \text{ value}) + (\text{ lower} \text{ class} \text{ boundary} \text{ value})}{2} \end{aligned} $$
Billing Data Statistics and Applications
Published in J. Lawrence, P.E. Vogt, Electricity Pricing, 2017
The central tendency, or average value, of a frequency distribution can be quantified by three different measures: the mode, the median, and the mean2. The mode for grouped data is simply the frequency of that interval which contains the most observations. For the bill distributions shown in Figure 10.3, the mode for the nonelectric heating customer bills is the 500 to 550 kWh (per bill) interval (with 4.35% of the total nonelectric heating service bills), while the mode for the electric heating customer bills is the 800 to 850 kWh interval (with 2.16% of the total electric heating service bills). A point estimate of the mode for grouped data can be determined by
Statistics – An introduction
Published in Allan Bonnick, Automotive Science and Mathematics, 2008
When summarising data, use may be made of classes, or groups. The number of items of data that fall into a class is called the class frequency. When data is presented in groups, as in Table 2.4, the data is referred to as grouped data. Although grouping data may destroy some of the detail in the original data an advantage is gained because the grouped data gives a very clear picture of patterns, which are an important part of statistical analysis.
A review of dispersion control charts for multivariate individual observations
Published in Quality Engineering, 2021
Jimoh Olawale Ajadi, Zezhong Wang, Inez Maria Zwetsloot
Multivariate dispersion control charts monitor the process variability of multiple correlated quality characteristics. The most common method for monitoring the covariance matrix of the process is the generalized variance chart proposed by Alt (1985). This chart applies the determinant of the estimated covariance matrix as the monitoring statistic. Over the past decades, many methods have been developed for monitoring the covariance matrix. To obtain an estimate of the covariance matrix, usually a sample of observations are collected. Here, is the number of correlated quality characteristics to be monitored. We refer to this as grouped data. For details on multivariate dispersion charts for grouped data, see the review articles by Yeh, Lin, and McGrath (2006) and Bersimis, Psarakis, and Panaretos (2007).
Uncertainty quantification: data assimilation, propagation and validation of the numerical model of the Arade river cable-stayed bridge
Published in Structure and Infrastructure Engineering, 2022
Iviane Cunha e Santos, José Luis Vital de Brito, Elsa de Sá Caetano
The descriptive statistics of response variable frequencies and simple statistical charts and tables for the grid model are summarised, including measures of location, dispersion, percentile, and outliers. Figure 19 illustrates a frequency distribution for grouped data. The distribution is asymmetric and negatively skewed. Most of the points tend to occur towards the upper end of the scale. Hence, in this set of points, the mean will be dragged lower than the median.