page_title: Box plot
section_title: Elements of a box plot
hierarchical_section_title: Box plot / Elements of a box plot
caption_attribution_description: English: Plot of a box-plot with whiskers to Min and Max of the Data. The plot was created with Statistica v.8.0 Deutsch: Zeichnung eines Box-Plot mit Whiskern, die vom Minimum bis zum Maximum der Daten reichen. Das Diagramm wurde mit Statistica v.8.0 erstellt.
context_page_description: In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending from the boxes indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points.
  Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution. The spacings between the different parts of the box indicate the degree of dispersion and skewness in the data, and show outliers. In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the interquartile range, midhinge, range, mid-range, and trimean. Box plots can be drawn either horizontally or vertically. Box plots received their name from the box in the middle.
context_section_description: 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 : the lowest data point excluding any outliers.
  Maximum : the largest data point excluding any outliers.
  Median (Q₂ / 50th percentile) : the middle value of the dataset.
  First quartile (Q₁ / 25th percentile) : also known as the lower quartile qₙ(0.25), is the  median of the lower half of the dataset. 
  Third quartile (Q₃ / 75th percentile) : also known as the upper quartile qₙ(0.75), is the median of the upper half of the dataset.
  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:
  Interquartile range (IQR) : is the distance between the upper and lower quartiles.
  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 Q₁ to Q₃ 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 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile and a whisker is drawn up to the lower observed point from the dataset that falls within this distance. All other observed points are plotted as outliers.
  However, the whiskers can represent several possible alternative values, among them:
  the minimum and maximum of all of the data (as in figure 2)
  one standard deviation above and below the mean of the data
  the 9th percentile and the 91st percentile
  the 2nd percentile and the 98th percentile.
  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.
  On some box plots a crosshatch is placed on each whisker, before the end of the whisker.
  Rarely, box plots can be presented with no whiskers at all.
  Because of this variability, it is appropriate to describe the convention being used for the whiskers and outliers in the caption for the plot.
  The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to show the seven-number summary. If the data are normally distributed, the locations of the seven marks on the box plot will be equally spaced.
caption: Figure 2. Boxplot with whiskers from minimum to maximum
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