A box plot is a statistical representation of the distribution of a variable through its quartiles. The ends of the box represent the lower and upper quartiles, while the median (second quartile) is marked by a line inside the box. For other statistical representations of numerical data, see other statistical charts.

Alternatives to box plots for visualizing distributions include histograms, violin plots, ECDF plots and strip charts.

Box Plot with `plotly.express`¶

Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on a variety of types of data and produces easy-to-style figures.

In a box plot created by px.box, the distribution of the column given as y argument is represented.

In [1]:

import plotly.express as px
df = px.data.tips()
fig = px.box(df, y="total_bill")
fig.show()

If a column name is given as x argument, a box plot is drawn for each value of x.

In [2]:

import plotly.express as px
df = px.data.tips()
fig = px.box(df, x="time", y="total_bill")
fig.show()

Box Plots in Dash¶

Dash is the best way to build analytical apps in Python using Plotly figures. To run the app below, run pip install dash, click "Download" to get the code and run python app.py.

Get started with the official Dash docs and learn how to effortlessly style & deploy apps like this with Dash Enterprise.

Out[3]:

Sign up for Dash Club → Free cheat sheets plus updates from Chris Parmer and Adam Schroeder delivered to your inbox every two months. Includes tips and tricks, community apps, and deep dives into the Dash architecture. Join now.

Display the underlying data¶

With the points argument, display underlying data points with either all points (all), outliers only (outliers, default), or none of them (False).

In [4]:

import plotly.express as px
df = px.data.tips()
fig = px.box(df, x="time", y="total_bill", points="all")
fig.show()

Choosing The Algorithm For Computing Quartiles¶

By default, quartiles for box plots are computed using the linear method (for more about linear interpolation, see #10 listed on http://jse.amstat.org/v14n3/langford.html and https://en.wikipedia.org/wiki/Quartile for more details).

However, you can also choose to use an exclusive or an inclusive algorithm to compute quartiles.

The exclusive algorithm uses the median to divide the ordered dataset into two halves. If the sample is odd, it does not include the median in either half. Q1 is then the median of the lower half and Q3 is the median of the upper half.

The inclusive algorithm also uses the median to divide the ordered dataset into two halves, but if the sample is odd, it includes the median in both halves. Q1 is then the median of the lower half and Q3 the median of the upper half.

In [5]:

import plotly.express as px

df = px.data.tips()

fig = px.box(df, x="day", y="total_bill", color="smoker")
fig.update_traces(quartilemethod="exclusive") # or "inclusive", or "linear" by default
fig.show()

Difference Between Quartile Algorithms¶

It can sometimes be difficult to see the difference between the linear, inclusive, and exclusive algorithms for computing quartiles. In the following example, the same dataset is visualized using each of the three different quartile computation algorithms.

In [6]:

import plotly.express as px
import pandas as pd

data = [1,2,3,4,5,6,7,8,9]
df = pd.DataFrame(dict(
    linear=data,
    inclusive=data,
    exclusive=data
)).melt(var_name="quartilemethod")


fig = px.box(df, y="value", facet_col="quartilemethod", color="quartilemethod",
             boxmode="overlay", points='all')

fig.update_traces(quartilemethod="linear", jitter=0, col=1)
fig.update_traces(quartilemethod="inclusive", jitter=0, col=2)
fig.update_traces(quartilemethod="exclusive", jitter=0, col=3)

fig.show()

Styled box plot¶

For the interpretation of the notches, see https://en.wikipedia.org/wiki/Box_plot#Variations.

In [7]:

import plotly.express as px
df = px.data.tips()
fig = px.box(df, x="time", y="total_bill", color="smoker",
             notched=True, # used notched shape
             title="Box plot of total bill",
             hover_data=["day"] # add day column to hover data
            )
fig.show()

Box plot with go.Box¶

If Plotly Express does not provide a good starting point, it is also possible to use the more generic go.Box class from plotly.graph_objects. All available options for go.Box are described in the reference page https://plotly.com/python/reference/box/.

Basic Box Plot¶

In [8]:

import plotly.graph_objects as go
import numpy as np
np.random.seed(1)

y0 = np.random.randn(50) - 1
y1 = np.random.randn(50) + 1

fig = go.Figure()
fig.add_trace(go.Box(y=y0))
fig.add_trace(go.Box(y=y1))

fig.show()

Basic Horizontal Box Plot¶

In [9]:

import plotly.graph_objects as go
import numpy as np

x0 = np.random.randn(50)
x1 = np.random.randn(50) + 2 # shift mean

fig = go.Figure()
# Use x instead of y argument for horizontal plot
fig.add_trace(go.Box(x=x0))
fig.add_trace(go.Box(x=x1))

fig.show()

Box Plot That Displays The Underlying Data¶

In [10]:

import plotly.graph_objects as go

fig = go.Figure(data=[go.Box(y=[0, 1, 1, 2, 3, 5, 8, 13, 21],
            boxpoints='all', # can also be outliers, or suspectedoutliers, or False
            jitter=0.3, # add some jitter for a better separation between points
            pointpos=-1.8 # relative position of points wrt box
              )])

fig.show()

Modifying The Algorithm For Computing Quartiles¶

For an explanation of how each algorithm works, see Choosing The Algorithm For Computing Quartiles.

In [11]:

import plotly.graph_objects as go

data = [1, 2, 3, 4, 5, 6, 7, 8, 9]

fig = go.Figure()
fig.add_trace(go.Box(y=data, quartilemethod="linear", name="Linear Quartile Mode"))
fig.add_trace(go.Box(y=data, quartilemethod="inclusive", name="Inclusive Quartile Mode"))
fig.add_trace(go.Box(y=data, quartilemethod="exclusive", name="Exclusive Quartile Mode"))
fig.update_traces(boxpoints='all', jitter=0)
fig.show()

Box Plot With Precomputed Quartiles¶

You can specify precomputed quartile attributes rather than using a built-in quartile computation algorithm.

This could be useful if you have already pre-computed those values or if you need to use a different algorithm than the ones provided.

In [12]:

import plotly.graph_objects as go

fig = go.Figure()

fig.add_trace(go.Box(q1=[ 1, 2, 3 ], median=[ 4, 5, 6 ],
                  q3=[ 7, 8, 9 ], lowerfence=[-1, 0, 1],
                  upperfence=[7, 8, 9], mean=[ 2.2, 2.8, 3.2 ],
                  sd=[ 0.2, 0.4, 0.6 ], notchspan=[ 0.2, 0.4, 0.6 ], name="Precompiled Quartiles"))

fig.show()

Colored Box Plot¶

In [13]:

import plotly.graph_objects as go
import numpy as np

y0 = np.random.randn(50)
y1 = np.random.randn(50) + 1 # shift mean

fig = go.Figure()
fig.add_trace(go.Box(y=y0, name='Sample A',
                marker_color = 'indianred'))
fig.add_trace(go.Box(y=y1, name = 'Sample B',
                marker_color = 'lightseagreen'))

fig.show()

Box Plot Styling Mean & Standard Deviation¶

In [14]:

import plotly.graph_objects as go

fig = go.Figure()
fig.add_trace(go.Box(
    y=[2.37, 2.16, 4.82, 1.73, 1.04, 0.23, 1.32, 2.91, 0.11, 4.51, 0.51, 3.75, 1.35, 2.98, 4.50, 0.18, 4.66, 1.30, 2.06, 1.19],
    name='Only Mean',
    marker_color='darkblue',
    boxmean=True # represent mean
))
fig.add_trace(go.Box(
    y=[2.37, 2.16, 4.82, 1.73, 1.04, 0.23, 1.32, 2.91, 0.11, 4.51, 0.51, 3.75, 1.35, 2.98, 4.50, 0.18, 4.66, 1.30, 2.06, 1.19],
    name='Mean & SD',
    marker_color='royalblue',
    boxmean='sd' # represent mean and standard deviation
))

fig.show()

Styling Outliers¶

The example below shows how to use the boxpoints argument. If "outliers", only the sample points lying outside the whiskers are shown. If "suspectedoutliers", the outlier points are shown and points either less than 4Q1-3Q3 or greater than 4Q3-3Q1 are highlighted (using outliercolor). If "all", all sample points are shown. If False, only the boxes are shown with no sample points.

In [15]:

import plotly.graph_objects as go

fig = go.Figure()
fig.add_trace(go.Box(
    y=[0.75, 5.25, 5.5, 6, 6.2, 6.6, 6.80, 7.0, 7.2, 7.5, 7.5, 7.75, 8.15,
       8.15, 8.65, 8.93, 9.2, 9.5, 10, 10.25, 11.5, 12, 16, 20.90, 22.3, 23.25],
    name="All Points",
    jitter=0.3,
    pointpos=-1.8,
    boxpoints='all', # represent all points
    marker_color='rgb(7,40,89)',
    line_color='rgb(7,40,89)'
))

fig.add_trace(go.Box(
    y=[0.75, 5.25, 5.5, 6, 6.2, 6.6, 6.80, 7.0, 7.2, 7.5, 7.5, 7.75, 8.15,
        8.15, 8.65, 8.93, 9.2, 9.5, 10, 10.25, 11.5, 12, 16, 20.90, 22.3, 23.25],
    name="Only Whiskers",
    boxpoints=False, # no data points
    marker_color='rgb(9,56,125)',
    line_color='rgb(9,56,125)'
))

fig.add_trace(go.Box(
    y=[0.75, 5.25, 5.5, 6, 6.2, 6.6, 6.80, 7.0, 7.2, 7.5, 7.5, 7.75, 8.15,
        8.15, 8.65, 8.93, 9.2, 9.5, 10, 10.25, 11.5, 12, 16, 20.90, 22.3, 23.25],
    name="Suspected Outliers",
    boxpoints='suspectedoutliers', # only suspected outliers
    marker=dict(
        color='rgb(8,81,156)',
        outliercolor='rgba(219, 64, 82, 0.6)',
        line=dict(
            outliercolor='rgba(219, 64, 82, 0.6)',
            outlierwidth=2)),
    line_color='rgb(8,81,156)'
))

fig.add_trace(go.Box(
    y=[0.75, 5.25, 5.5, 6, 6.2, 6.6, 6.80, 7.0, 7.2, 7.5, 7.5, 7.75, 8.15,
        8.15, 8.65, 8.93, 9.2, 9.5, 10, 10.25, 11.5, 12, 16, 20.90, 22.3, 23.25],
    name="Whiskers and Outliers",
    boxpoints='outliers', # only outliers
    marker_color='rgb(107,174,214)',
    line_color='rgb(107,174,214)'
))


fig.update_layout(title_text="Box Plot Styling Outliers")
fig.show()

Grouped Box Plots¶

In [16]:

import plotly.graph_objects as go

x = ['day 1', 'day 1', 'day 1', 'day 1', 'day 1', 'day 1',
     'day 2', 'day 2', 'day 2', 'day 2', 'day 2', 'day 2']

fig = go.Figure()

fig.add_trace(go.Box(
    y=[0.2, 0.2, 0.6, 1.0, 0.5, 0.4, 0.2, 0.7, 0.9, 0.1, 0.5, 0.3],
    x=x,
    name='kale',
    marker_color='#3D9970'
))
fig.add_trace(go.Box(
    y=[0.6, 0.7, 0.3, 0.6, 0.0, 0.5, 0.7, 0.9, 0.5, 0.8, 0.7, 0.2],
    x=x,
    name='radishes',
    marker_color='#FF4136'
))
fig.add_trace(go.Box(
    y=[0.1, 0.3, 0.1, 0.9, 0.6, 0.6, 0.9, 1.0, 0.3, 0.6, 0.8, 0.5],
    x=x,
    name='carrots',
    marker_color='#FF851B'
))

fig.update_layout(
    yaxis_title='normalized moisture',
    boxmode='group' # group together boxes of the different traces for each value of x
)
fig.show()

Grouped Horizontal Box Plot¶

In [17]:

import plotly.graph_objects as go

y = ['day 1', 'day 1', 'day 1', 'day 1', 'day 1', 'day 1',
     'day 2', 'day 2', 'day 2', 'day 2', 'day 2', 'day 2']

fig = go.Figure()
fig.add_trace(go.Box(
    x=[0.2, 0.2, 0.6, 1.0, 0.5, 0.4, 0.2, 0.7, 0.9, 0.1, 0.5, 0.3],
    y=y,
    name='kale',
    marker_color='#3D9970'
))
fig.add_trace(go.Box(
    x=[0.6, 0.7, 0.3, 0.6, 0.0, 0.5, 0.7, 0.9, 0.5, 0.8, 0.7, 0.2],
    y=y,
    name='radishes',
    marker_color='#FF4136'
))
fig.add_trace(go.Box(
    x=[0.1, 0.3, 0.1, 0.9, 0.6, 0.6, 0.9, 1.0, 0.3, 0.6, 0.8, 0.5],
    y=y,
    name='carrots',
    marker_color='#FF851B'
))

fig.update_layout(
    xaxis=dict(title='normalized moisture', zeroline=False),
    boxmode='group'
)

fig.update_traces(orientation='h') # horizontal box plots
fig.show()

Rainbow Box Plots¶

In [18]:

import plotly.graph_objects as go
import numpy as np

N = 30     # Number of boxes

# generate an array of rainbow colors by fixing the saturation and lightness of the HSL
# representation of colour and marching around the hue.
# Plotly accepts any CSS color format, see e.g. http://www.w3schools.com/cssref/css_colors_legal.asp.
c = ['hsl('+str(h)+',50%'+',50%)' for h in np.linspace(0, 360, N)]

# Each box is represented by a dict that contains the data, the type, and the colour.
# Use list comprehension to describe N boxes, each with a different colour and with different randomly generated data:
fig = go.Figure(data=[go.Box(
    y=3.5 * np.sin(np.pi * i/N) + i/N + (1.5 + 0.5 * np.cos(np.pi*i/N)) * np.random.rand(10),
    marker_color=c[i]
    ) for i in range(int(N))])

# format the layout
fig.update_layout(
    xaxis=dict(showgrid=False, zeroline=False, showticklabels=False),
    yaxis=dict(zeroline=False, gridcolor='white'),
    paper_bgcolor='rgb(233,233,233)',
    plot_bgcolor='rgb(233,233,233)',
)

fig.show()

Fully Styled Box Plots¶

In [19]:

import plotly.graph_objects as go

x_data = ['Carmelo Anthony', 'Dwyane Wade',
          'Deron Williams', 'Brook Lopez',
          'Damian Lillard', 'David West',]

N = 50

y0 = (10 * np.random.randn(N) + 30).astype(int)
y1 = (13 * np.random.randn(N) + 38).astype(int)
y2 = (11 * np.random.randn(N) + 33).astype(int)
y3 = (9 * np.random.randn(N) + 36).astype(int)
y4 = (15 * np.random.randn(N) + 31).astype(int)
y5 = (12 * np.random.randn(N) + 40).astype(int)

y_data = [y0, y1, y2, y3, y4, y5]

colors = ['rgba(93, 164, 214, 0.5)', 'rgba(255, 144, 14, 0.5)', 'rgba(44, 160, 101, 0.5)',
          'rgba(255, 65, 54, 0.5)', 'rgba(207, 114, 255, 0.5)', 'rgba(127, 96, 0, 0.5)']

fig = go.Figure()

for xd, yd, cls in zip(x_data, y_data, colors):
        fig.add_trace(go.Box(
            y=yd,
            name=xd,
            boxpoints='all',
            jitter=0.5,
            whiskerwidth=0.2,
            fillcolor=cls,
            marker_size=2,
            line_width=1)
        )

fig.update_layout(
    title='Points Scored by the Top 9 Scoring NBA Players in 2012',
    yaxis=dict(
        autorange=True,
        showgrid=True,
        zeroline=True,
        dtick=5,
        gridcolor='rgb(255, 255, 255)',
        gridwidth=1,
        zerolinecolor='rgb(255, 255, 255)',
        zerolinewidth=2,
    ),
    margin=dict(
        l=40,
        r=30,
        b=80,
        t=100,
    ),
    paper_bgcolor='rgb(243, 243, 243)',
    plot_bgcolor='rgb(243, 243, 243)',
    showlegend=False
)

fig.show()

Box Plot With Only Points¶

A strip chart is like a box plot with points showing, and no box:

In [20]:

import plotly.express as px
df = px.data.tips()
fig = px.strip(df, x='day', y='tip')
fig.show()

Reference¶

See function reference for px.box() or https://plotly.com/python/reference/box/ for more information and chart attribute options!

What About Dash?¶

Dash is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library.

Learn about how to install Dash at https://dash.plot.ly/installation.

Everywhere in this page that you see fig.show(), you can display the same figure in a Dash application by passing it to the figure argument of the Graph component from the built-in dash_core_components package like this:

import plotly.graph_objects as go # or plotly.express as px
fig = go.Figure() # or any Plotly Express function e.g. px.bar(...)
# fig.add_trace( ... )
# fig.update_layout( ... )

from dash import Dash, dcc, html

app = Dash()
app.layout = html.Div([
    dcc.Graph(figure=fig)
])

app.run_server(debug=True, use_reloader=False)  # Turn off reloader if inside Jupyter

Box Plot with plotly.express¶