Update box plots doc with precomputed quartiles and quartilemethod

doc/python/box-plots.md

@@ -71,6 +71,49 @@ 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 a linear algorithm method (see #10 listed on [http://www.amstat.org/publications/jse/v14n3/langford.html](http://www.amstat.org/publications/jse/v14n3/langford.html) 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", boxmode="overlay", color="quartilemethod")
+
+fig.update_traces(quartilemethod="linear", col=1)
+fig.update_traces(quartilemethod="inclusive", col=2)
+fig.update_traces(quartilemethod="exclusive", col=3)
+
+fig.show()
+```
+
 #### Styled box plot
 
 For the interpretation of the notches, see https://en.wikipedia.org/wiki/Box_plot#Variations.
@@ -124,7 +167,7 @@ fig.add_trace(go.Box(x=x1))
 fig.show()
 ```
 
-### Box Plot That Displays the Underlying Data
+### Box Plot That Displays The Underlying Data
 
 ```python
 import plotly.graph_objects as go
@@ -138,6 +181,45 @@ fig = go.Figure(data=[go.Box(y=[0, 1, 1, 2, 3, 5, 8, 13, 21],
 fig.show()
 ```
 
+### 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.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(y=[
+        [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
+        [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
+        [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
+      ], name="Precompiled Quartiles"))
+
+fig.update_traces(q1=[ 1, 2, 3 ], median=[ 4, 5, 6 ], 
+                  q3=[ 7, 8, 9 ], lowerfence=[-1, 0, 1], 
+                  upperfence=[5, 6, 7], mean=[ 2.2, 2.8, 3.2 ], 
+                  sd=[ 0.2, 0.4, 0.6 ], notchspan=[ 0.2, 0.4, 0.6 ] )
+
+fig.show()
+```
+
 ### Colored Box Plot
 
 ```python