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Mean, median, mode and standard deviation
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
Other measures of dispersion which are sometimes used are the quartile, decile and percentile values. The quartile values of a set of discrete data are obtained by selecting the values of members which divide the set into four equal parts. Thus, for the set {2,3,4,5,5,7,9,11,13,14,17} there are 11 members and the values of the members dividing the set into four equal parts are 4,7 and 13. These values are signified by Q1,Q2 and Q3 and called the first, second and third quartile values, respectively. It can be seen that the second quartile value, Q2, is the value of the middle member and hence is the median value of the set.
Robust estimation and representation of climatic wave spectrum
Published in C. Guedes Soares, T.A. Santos, Progress in Maritime Technology and Engineering, 2018
G. Rodriguez, G. Clarindo, C. Guedes Soares
Information provided by quartiles can be used to generate a clear and compact visual representation of the sample distribution known as boxplot, a graphical tool which strikingly summarize and display the distribution of a set of continuous data (Tukey, 1977). However, in its most common version, also known as box-and-whisker plot, the thin lines drawn from the edges of the box do not reach the extremes but up to some inner boundaries named as whiskers, which can be defined in various ways. Particularly, in this study, the whisker boundaries have been placed at D1 and D9, but can be changed by some other couple of percentiles (e.g. 5th and 95th or 1th and 99th). Note that the box emphasizes the part of the data set where the middle 50% of the data lie, whereas whiskers provides information on that part of the data set which lies in the usually large intervals between the quartiles and these boundaries, in this case the middle 80%. Further details on the construction of a boxplot can be found in many statistical reference books (e.g., Hoaglin, et al., 1983).
Water Quality and Monitoring
Published in Yeqiao Wang, Fresh Water and Watersheds, 2020
A trend is a persistent change in the water quality variable(s) of interest over time. Trend stations are single independent watersheds where a group of treatments might be implemented gradually over time or where the response might take a long time. A control watershed for trend detection is needed to distinguish climate trends. It is generally recommended to perform several different techniques before reaching a conclusion,[12] such as 1) a time plot, 2) a least-square fit regression, 3) comparison of annual means, 4) comparing cumulative distribution curves, 5) comparing quartiles (Q–Q plot), 6) double mass analysis, 7) paired regressions, 8) time series analysis, and 9) the seasonal Kendall test.[13]
Can you see the feel? The absence of tactile cues in clothing e-commerce impairs consumer decision making
Published in International Journal of Fashion Design, Technology and Education, 2023
Julia Wilfling, George Havenith, Margherita Raccuglia, Simon Hodder
To assess differences between the visual only and visual and haptic information data were checked for normal distribution. The data deviated from a normal distribution and differences were, therefore, tested using a Wilcoxon signed rank test (between subjects). A Kruskal–Wallis test was performed to look at differences in the perception of textiles between males and females. Dependent variables were defined as the textile attributes (rough, smooth, soft, etc.), the factor variable was sex. The medians of the data were calculated together with the 25th and 75th quartile. The median is less affected by outliers and skewed data and makes it a better option to measure the central tendency of respondents. Statistical analysis was performed using IBM SPSS Statistics 24 (IBM, USA). A probability level of p < 0.05 was defined as the threshold for significance.
Travellers’ perspectives on historic squares and railway stations in Italian heritage cities revealed through sentiment analysis
Published in Journal of Urban Design, 2023
Stefania Stellacci, Sérgio Moro
Approximately 43,000 online reviews about 10 public spaces in Italian heritage cities are analysed against 6 evaluation categories (Table 2, 1st column). For each of these categories, single topics and related adjectives (Table 2, 4th column) are grouped to integrate and ease data visualization. These data are visually organized using boxplots (groups of numerical sentiment score in quartiles) in Figures 2–4 to map anomalies (signs of skewness), dispersion (outliers plotted as individual points and discarded from the data series), and the position of the median value (indicated in bolded line). The interquartile range (IQR) represents the variability about the median, the lower quartile: Q1 – 1.5*IQR and upper quartile: Q2 = Q3 + 1.5*IQR. The whiskers connect the quartiles to the minimum and maximum values. In case of heterogenous opinions of the reviewers, the IQR is displayed as a long box.
Method for automated detection of outliers in crash simulations
Published in International Journal of Crashworthiness, 2023
David Kracker, Revan Kumar Dhanasekaran, Axel Schumacher, Jochen Garcke
Another well-known method, which is more robust towards outliers, stems from the visualization by box plots [17,18]. The basis for this is the interquartile range. First, the data are sorted in ascending order by their value. The first and third quartiles are determined within which 25% and 75% of the data lie, respectively. The difference between the first and third quartile is called the interquartile range (IQR). In a boxplot, these two values mark the position of the box. Data points that are more than 1.5 times the IQR away from the third quartile of the data are marked as outliers. At this distance, the so-called whiskers are drawn in the boxplot. In the following, this method will be referred to as the IQR method. If more than 25% of the data consist of outliers the calculation of the threshold is affected.