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The Box Erklärung

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The Box Erklärung
The Box Erklärung

The range-bar was introduced by Mary Eleanor Spear in [1] and again in A boxplot is a standardized way of displaying the dataset based on a five-number summary : the minimum, the maximum, the sample median, and the first and third quartiles.

Minimum Q 0 or 0th percentile : the lowest data point excluding any outliers. Maximum Q 4 or th percentile : the largest data point excluding any outliers.

First quartile Q 1 or 25th percentile : also known as the lower quartile q n 0. Third quartile Q 3 or 75th percentile : also known as the upper quartile q n 0.

An important element used to construct the box plot by determining the minimum and maximum data values feasible, but is not part of the aforementioned five-number summary, is the interquartile range or IQR denoted below:.

A boxplot is constructed of two parts, a box and a set of whiskers shown in Figure 2. The lowest point is the minimum of the data set and the highest point is the maximum of the data set.

The box is drawn from Q 1 to Q 3 with a horizontal line drawn in the middle to denote the median. The same data set can also be represented as a boxplot shown in Figure 3.

From above the upper quartile, a distance of 1. Similarly, a distance of 1. All other observed points are plotted as outliers. Any data not included between the whiskers should be plotted as an outlier with a dot, small circle, or star, but occasionally this is not done.

Some box plots include an additional character to represent the mean of the data. Because of this variability, it is appropriate to describe the convention being used for the whiskers and outliers in the caption for the plot.

If the data are normally distributed , the locations of the seven marks on the box plot will be equally spaced. Since the mathematician John W.

Tukey popularized this type of visual data display in , several variations on the traditional box plot have been described. Variable width box plots illustrate the size of each group whose data is being plotted by making the width of the box proportional to the size of the group.

A popular convention is to make the box width proportional to the square root of the size of the group. Notched box plots apply a "notch" or narrowing of the box around the median.

Notches are useful in offering a rough guide to significance of difference of medians; if the notches of two boxes do not overlap, this offers evidence of a statistically significant difference between the medians.

However, there is uncertainty about the most appropriate multiplier as this may vary depending on the similarity of the variances of the samples.

Adjusted box plots are intended for skew distributions. Save Word. Other Words from box Synonyms Learn More about box.

Keep scrolling for more. First Known Use of box Noun 1 before the 12th century, in the meaning defined at sense 1 Verb 1 15th century, in the meaning defined at sense 1 Verb 2 , in the meaning defined at transitive sense 1 Noun 2 15th century, in the meaning defined above Noun 3 before the 12th century, in the meaning defined above Verb 3 , in the meaning defined above.

History and Etymology for box Noun 1 Middle English, from Old English, from Late Latin buxis , from Greek pyxis , from pyxos box tree Noun 2 Middle English Noun 3 Middle English, from Old English, from Latin buxus , from Greek pyxos Verb 3 probably from Spanish bojar to circumnavigate, from Catalan vogir to turn, from Latin volvere to roll — more at voluble.

Learn More about box. Share box Post the Definition of box to Facebook Share the Definition of box on Twitter. Time Traveler for box The first known use of box was before the 12th century See more words from the same century.

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