Box plot
A box plot is a method used in descriptive statistics to graphically depict numerical data groups
via their quadrilles. Box plots may also have lines extending from the boxes (whiskers) indicating
variability outside the upper and lower quadrilles, hence the terms box-and-whisker plot and
box-and-whisker diagram.
Outliers can be plotted as single points. Box plots are non-parametric:
they show variance in statistical population samples without making any assumptions about the
underlying statistical distribution (although Turkey's box plot assumes symmetry for whiskers
and normality for their length). The spacing between the various box parts indicates the degree
of dispersion (spread)
And novelty in the data, and outliers show. Aside from the points
themselves, they allow one to estimate various L-estimators visually, notably the quarter-final
range, mid-hinge, range, mid-range, and Crimean. Plots of boxes can be drawn either vertically
or horizontally. Box plots got their name in the middle of the box.
Elements of a box plot
A boxplot is a standardized way of displaying the data set based on a five-number summary: the
minimum, the maximum, the sample median, the first and third quartile. Minimum: The lowest
point of data that excludes outliers. Maximum: the most extensive data point that excludes
outliers. Median (Q2/50th percentile): Middle value of the Dataset.
First
quartile (Q1/25th percentile): also known as an (0.25) lower quartile, is the lower half of the
dataset median. Third quartile (Q3/75th percentile): also known as
(0.75) upper quartile, is the
top half of the sample mean.
The interquartile range or IQR denoted below is an important element used to construct the
box plot by determining the feasible minimum and maximum data values but is not part of the
aforementioned five-number summary:
Interquartile Range (IQR): is the distance from the upper quartile to the lower.
{IQR
= Q3-Q1 = q {n} (0.75)-q {n} (0.25)}{\display style IQR = Q3-Q1 = q {n} (0.75)-q {n} (0.25)}}}
A boxplot consists of two parts, a box and a group of whiskers depicted. The lowest point is the
dataset minimum, and the highest point is the data set maximum. The box is drawn between Q1
and Q3 with a horizontal line in the middle to denote the median.

This can also reflect the same set of data as a boxplot seen. A distance of 1.5 times the IQR is

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- Interquartile range, Quartile