---
jupyter:
  jupytext:
    notebook_metadata_filter: all
    text_representation:
      extension: .md
      format_name: markdown
      format_version: '1.3'
      jupytext_version: 1.14.1
  kernelspec:
    display_name: Python 3 (ipykernel)
    language: python
    name: python3
  language_info:
    codemirror_mode:
      name: ipython
      version: 3
    file_extension: .py
    mimetype: text/x-python
    name: python
    nbconvert_exporter: python
    pygments_lexer: ipython3
    version: 3.8.8
  plotly:
    description: How to make Box Plots in Python with Plotly.
    display_as: statistical
    language: python
    layout: base
    name: Box Plots
    order: 2
    page_type: example_index
    permalink: python/box-plots/
    redirect_from:
    - /python/box/
    - /python/basic_statistics/
    thumbnail: thumbnail/box.jpg
---

<!-- #region -->
A [box plot](https://en.wikipedia.org/wiki/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](https://plotly.com/python/statistical-charts/).


Alternatives to box plots for visualizing distributions include [histograms](https://plotly.com/python/histograms/), [violin plots](https://plotly.com/python/violin/), [ECDF plots](https://plotly.com/python/ecdf-plots/) and [strip charts](https://plotly.com/python/strip-charts/).

## Box Plot with `plotly.express`

[Plotly Express](/python/plotly-express/) is the easy-to-use, high-level interface to Plotly, which [operates on a variety of types of data](/python/px-arguments/) and produces [easy-to-style figures](/python/styling-plotly-express/).

In a box plot created by `px.box`, the distribution of the column given as `y` argument is represented.
<!-- #endregion -->

```python
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`.

```python
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](https://plotly.com/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](https://dash.plotly.com/installation) and **learn how to effortlessly [style](https://plotly.com/dash/design-kit/) & [deploy](https://plotly.com/dash/app-manager/) apps like this with <a class="plotly-red" href="https://plotly.com/dash/">Dash Enterprise</a>.**

```python hide_code=true
from IPython.display import IFrame
snippet_url = 'https://python-docs-dash-snippets.herokuapp.com/python-docs-dash-snippets/'
IFrame(snippet_url + 'box-plots', width='100%', height=1200)
```

<div style="font-size: 0.9em;"><div style="width: calc(100% - 30px); box-shadow: none; border: thin solid rgb(229, 229, 229);"><div style="padding: 5px;"><div><p><strong>Sign up for Dash Club</strong> → 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.
<u><a href="https://go.plotly.com/dash-club?utm_source=Dash+Club+2022&utm_medium=graphing_libraries&utm_content=inline">Join now</a></u>.</p></div></div></div></div>


### 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`).

```python
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](http://jse.amstat.org/v14n3/langford.html) and [https://en.wikipedia.org/wiki/Quartile](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.

```python
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.

```python
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.

```python
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`](/python/graph-objects/). All available options for `go.Box` are described in the reference page https://plotly.com/python/reference/box/.

### Basic Box Plot

```python
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

```python
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

```python
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](#choosing-the-algorithm-for-computing-quartiles).

```python
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.

```python
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

```python
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

```python
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.

```python
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

```python
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=dict(
        title=dict(
            text='normalized moisture')
    ),
    boxmode='group' # group together boxes of the different traces for each value of x
)
fig.show()
```

### Grouped Horizontal Box Plot

```python
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=dict(text='normalized moisture'), zeroline=False),
    boxmode='group'
)

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

### Rainbow Box Plots

```python
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

```python
import plotly.graph_objects as go
import numpy as np

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=dict(text='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](/python/strip-charts/) is like a box plot with points showing, and no box:

```python
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()`](https://plotly.com/python-api-reference/generated/plotly.express.box) or https://plotly.com/python/reference/box/ for more information and chart attribute options!
