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Introductory Statistics Refresher
Published in Jiro Nagatomi, Eno Essien Ebong, Mechanobiology Handbook, 2018
Julia L. Sharp, Patrick D. Gerard
A box-and-whisker plot can be used to visualize the distribution of a quantitative variable and compare distributions for several levels of a qualitative variable. A box-and-whisker plot is a plot of the five-number summary, where the five numbers are the minimum, the first quartile, the median, the third quartile, and the maximum. Software packages will often discern extreme values in box-and-whisker plots using Tukey's “fences,” or the number of interquartile ranges that an observation is away from the first and third quartile (Hoaglin, 2003). The most typically used “fence” to identify extreme observations is 1.5 × IQR. If an observation in the data is less than Q1 – 1.5 × IQR, the observation is marked separately on the box-and-whisker plot. Likewise, if an observation is more than Q3 + 1.5 × IQR, the observation is marked separately on the box-and-whisker plot. Because there are few observations per level in the study described in Example 4.1, only a single box-and-whisker plot will be created for the normalized fluorescence values (Figure 4.2a). There are no extreme observations identified using Tukey's method of constructing fences. If there were extreme observations identified using Tukey's method, the plot would show a single point (or multiple points if there were multiple extreme observations) on the plot more extreme than the minimum and/or maximum values (Figure 4.2b).
Track
Published in Walter R. Paczkowski, Deep Data Analytics for New Product Development, 2020
The last five are known as the Five Number Summary, a robust set of statistics unaffected by distribution skewness. Although unaffected, they help determine skewness and symmetry of the data distribution: Symmetric: (75% – 50%) = (50% – 25%)Right-Skewed: (75% – 50%) > (50% – 25%)Left Skewed: (75% – 50%) < (50% – 25%)
Presenting and Using Assessment Results
Published in Charles Yoe, Principles of Risk Analysis, 2019
The five-number summary provides an easy and concise summary of the distribution of the observations without resorting to using the mean. Consistently reporting these five numbers avoids both anchoring to a mean as well as the need to focus on any one summary statistic. The five-number summary is useful because it provides information about the location of the data with the median. The data's spread is described by the quartiles, and extreme values are estimated by the minimum and maximum observations. The data range and interquartile range (middle 50% of all observations) are easily calculated from the five-number summary.
Compressive strength of geopolymer concrete composites: a systematic comprehensive review, analysis and modeling
Published in European Journal of Environmental and Civil Engineering, 2023
Hemn Unis Ahmed, Ahmed S. Mohammed, Shaker M. A. Qaidi, Rabar H. Faraj, Nadhim Hamah Sor, Azad A. Mohammed
A boxplot is a standardized method for representing the distribution of data using a five-number summary (‘minimum’, first (lower) quartile (Q1), median, third (upper) quartile (Q3), and ‘maximum’). It can provide information about your outliers and their values. Additionally, it can determine whether your data is symmetrical, how densely your data is clustered, and whether and how your data is skewed. Therefore, the box plot in Figure 33 was also used to validate the model performance for FA-GPC's measured and predicted compressive strength. Between the first and third quartiles, a box plot is constructed. The line inside the box shows the median, and the whiskers extend to the box minimum and maximum values from both ends. Thus, a box and whisker plot is a distribution graph; it depicts how data are distributed around the median, skewed, or symmetrical. The results indicated that the ANN model has a better performance than the other models because the box plot of ANN datasets had the same pattern for the minimum and maximum CS values, mean and median.
A two-state, multi-criteria Markov chain model for stochastic solar generators
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Nedjma Abdelhafidi, Ali Cheknane, Nour El Islam Bachari, Majid Almaraashi, Michel Aillerie
The three percentiles (25%, 50%, and 75%) and the minimum and maximum values of the datasets allow the composition of a five-number summary. A box plot is one way of graphically depicting a dataset’s five-number summary (Figure 6).