boxchart
Box chart (box plot)
Syntax
Description
boxchart(
creates a box chart, or box
plot, for each column of the matrix ydata
)ydata
. If
ydata
is a vector, then boxchart
creates a
single box chart.
Each box chart displays the following information: the median, the lower and upper quartiles, any outliers (computed using the interquartile range), and the minimum and maximum values that are not outliers. For more information, see Box Chart (Box Plot).
boxchart(
groups the data in the vector xgroupdata
,ydata
)ydata
according to the unique values in
xgroupdata
and plots each group of data as a separate box chart.
xgroupdata
determines the position of each box chart along the
xaxis. ydata
must be a vector, and
xgroupdata
must have the same length as
ydata
.
boxchart(___,'GroupByColor',
uses color to differentiate between box charts. The software groups the data in the vector
cgroupdata
)ydata
according to the unique value combinations in
xgroupdata
(if specified) and cgroupdata
, and
plots each group of data as a separate box chart. The vector
cgroupdata
then determines the color of each box chart.
ydata
must be a vector, and cgroupdata
must
have the same length as ydata
. Specify the
'GroupByColor'
namevalue pair argument after any of the input
argument combinations in the previous syntaxes.
boxchart(___,
specifies additional chart options using one or more namevalue pair arguments. For
example, you can compare sample medians using notches by specifying
Name,Value
)'Notch','on'
. Specify the namevalue pair arguments after all other
input arguments. For a list of properties, see BoxChart Properties.
returns
b
= boxchart(___)BoxChart
objects. If you do not specify
cgroupdata
, then b
contains one object. If you
do specify it, then b
contains a vector of objects, one for each
unique value in cgroupdata
. Use b
to set
properties of the box charts after creating them. For a list of properties, see BoxChart Properties.
Examples
Create Box Chart from Vector Data
Create a single box chart from a vector of ages. Use the box chart to visualize the distribution of ages.
Load the patients
data set. The Age
variable contains the ages of 100 patients. Create a box chart to visualize the distribution of ages.
load patients boxchart(Age) ylabel('Age (years)')
The median patient age of 39 years is shown as the line inside the box. The lower and upper quartiles of 32 and 44 years are shown as the bottom and top edges of the box, respectively. The whiskers, or lines that extend below and above the box, have endpoints that correspond to the youngest and oldest patients. The youngest patient is 25 years old, and the oldest is 50 years old. The data set contains no outliers, which would be represented by small circles.
You can use data tips to get a summary of the data statistics. Hover over the box chart to see the data tip.
Create Box Charts from Matrix Data
Use box charts to compare the distribution of values along the columns and the rows of a magic square.
Create a magic square with 10 rows and 10 columns.
Y = magic(10)
Y = 10×10
92 99 1 8 15 67 74 51 58 40
98 80 7 14 16 73 55 57 64 41
4 81 88 20 22 54 56 63 70 47
85 87 19 21 3 60 62 69 71 28
86 93 25 2 9 61 68 75 52 34
17 24 76 83 90 42 49 26 33 65
23 5 82 89 91 48 30 32 39 66
79 6 13 95 97 29 31 38 45 72
10 12 94 96 78 35 37 44 46 53
11 18 100 77 84 36 43 50 27 59
Create a box chart for each column of the magic square. Each column has a similar median value (around 50
). However, the first five columns of Y
have greater interquartile ranges than the last five columns of Y
. The interquartile range is the distance between the upper quartile (top edge of the box) and the lower quartile (bottom edge of the box).
boxchart(Y) xlabel('Column') ylabel('Value')
Create a box chart for each row of the magic square. Each row has a similar interquartile range, but the median values differ across the rows.
boxchart(Y') xlabel('Row') ylabel('Value')
Create Multiple Box Charts Using Positional Grouping Variable
Plot the magnitudes of earthquakes according to the month in which they occurred. Use a vector of earthquake magnitudes and a grouping variable indicating the month of each earthquake. For each group of data, create a box chart and place it in the specified position along the xaxis.
Read a set of tsunami data into the workspace as a table. The data set includes information on earthquakes as well as other causes of tsunamis. Display the first eight rows, showing the month, cause, and earthquake magnitude columns of the table.
tsunamis = readtable('tsunamis.xlsx'); tsunamis(1:8,["Month","Cause","EarthquakeMagnitude"])
ans=8×3 table
Month Cause EarthquakeMagnitude
_____ __________________ ___________________
10 {'Earthquake' } 7.6
8 {'Earthquake' } 6.9
12 {'Volcano' } NaN
3 {'Earthquake' } 8.1
3 {'Earthquake' } 4.5
5 {'Meteorological'} NaN
11 {'Earthquake' } 9
3 {'Earthquake' } 5.8
Create the table earthquakes
, which contains data for the tsunamis caused by earthquakes.
unique(tsunamis.Cause)
ans = 8x1 cell
{0x0 char }
{'Earthquake' }
{'Earthquake and Landslide'}
{'Landslide' }
{'Meteorological' }
{'Unknown Cause' }
{'Volcano' }
{'Volcano and Landslide' }
idx = contains(tsunamis.Cause,'Earthquake');
earthquakes = tsunamis(idx,:);
Group the earthquake magnitudes based on the month in which the corresponding tsunamis occurred. For each month, display a separate box chart. For example, boxchart
uses the fourth, fifth, and eighth earthquake magnitudes, as well as others, to create the third box chart, which corresponds to the third month.
boxchart(earthquakes.Month,earthquakes.EarthquakeMagnitude) xlabel('Month') ylabel('Earthquake Magnitude')
Notice that because the month values are numeric, the xaxis ruler is also numeric.
For more descriptive month names, convert the earthquakes.Month
column to a categorical
variable.
monthOrder = ["Jan","Feb","Mar","Apr","May","Jun","Jul", ... "Aug","Sep","Oct","Nov","Dec"]; namedMonths = categorical(earthquakes.Month,1:12,monthOrder);
Create the same box charts as before, but use the categorical
variable namedMonths
instead of the numeric month values. The xaxis ruler is now categorical, and the order of the categories in namedMonths
determines the order of the box charts.
boxchart(namedMonths,earthquakes.EarthquakeMagnitude) xlabel('Month') ylabel('Earthquake Magnitude')
Bin Data to Create Grouping Variable
Group medical patients based on their age, and for each age group, create a box chart of diastolic blood pressure values.
Load the patients
data set. The Age
and Diastolic
variables contain the ages and diastolic blood pressure levels of 100 patients.
load patients
Group the patients into five age bins. Find the minimum and maximum ages, and then divide the range between them into fiveyear bins. Bin the values in the Age
variable by using the discretize
function. Use the bin names in bins
. The resulting groupAge
variable is a categorical
variable.
min(Age)
ans = 25
max(Age)
ans = 50
binEdges = 25:5:50; bins = {'late 20s','early 30s','late 30s','early 40s','late 40s+'}; groupAge = discretize(Age,binEdges,'categorical',bins);
Create a box chart for each age group. Each box chart shows the diastolic blood pressure values of the patients in that group.
boxchart(groupAge,Diastolic) xlabel('Age Group') ylabel('Diastolic Blood Pressure')
Use Positional and Color Grouping Variables
Use two grouping variables to group data and to position and color the resulting box charts.
Load the sample file TemperatureData.csv
, which contains average daily temperatures from January 2015 through July 2016. Read the file into a table.
tbl = readtable('TemperatureData.csv');
Convert the tbl.Month
variable to a categorical
variable. Specify the order of the categories.
monthOrder = {'January','February','March','April','May','June','July', ... 'August','September','October','November','December'}; tbl.Month = categorical(tbl.Month,monthOrder);
Create box charts showing the distribution of temperatures during each month of each year. Specify tbl.Month
as the positional grouping variable. Specify tbl.Year
as the color grouping variable by using the 'GroupByColor'
namevalue pair argument. Notice that tbl
does not contain data for some months of 2016.
boxchart(tbl.Month,tbl.TemperatureF,'GroupByColor',tbl.Year) ylabel('Temperature (F)') legend
In this figure, you can easily compare the distribution of temperatures for one particular month across multiple years. For example, you can see that February temperatures varied much more in 2016 than in 2015.
Plot Mean over Box Charts
Create box charts, and plot the mean values over the box charts by using hold on
.
Load the patients
data set. Convert SelfAssessedHealthStatus
to an ordinal categorical
variable because the categories Poor
, Fair
, Good
, and Excellent
have a natural order.
load patients healthOrder = {'Poor','Fair','Good','Excellent'}; SelfAssessedHealthStatus = categorical(SelfAssessedHealthStatus, ... healthOrder,'Ordinal',true);
Group the patients according to their selfassessed health status, and find the mean patient weight for each group.
meanWeight = groupsummary(Weight,SelfAssessedHealthStatus,'mean');
Compare the weights for each group of patients by using box charts. Plot the mean weights over the box charts.
boxchart(SelfAssessedHealthStatus,Weight) hold on plot(meanWeight,'o') hold off legend(["Weight Data","Weight Mean"])
Compare Medians Using Notches
Use notches to determine whether median values are significantly different from each other.
Load the patients
data set. Split the patients according to their location. For each group of patients, create a box chart of their weights. Specify 'Notch','on'
so that each box includes a tapered, shaded region called a notch. Box charts whose notches do not overlap have different medians at the 5% significance level.
load patients boxchart(categorical(Location),Weight,'Notch','on') ylabel('Weight (lbs)')
In this example, the three notches overlap, showing that the three weight medians are not significantly different.
Specify Axes for Box Charts
Display a sidebyside pair of box charts using the tiledlayout
and nexttile
functions.
Load the patients
data set. Convert Smoker
to a categorical
variable with the descriptive category names Smoker
and Nonsmoker
rather than 1
and 0
.
load patients Smoker = categorical(Smoker,logical([1 0]),{'Smoker','Nonsmoker'});
Create a 1by2 tiled chart layout using the tiledlayout
function. Create the first set of axes ax1
within it by calling the nexttile
function. In the first set of axes, display two box charts of systolic blood pressure values, one for smokers and the other for nonsmokers. Create the second set of axes ax2
within the tiled chart layout by calling the nexttile
function. In the second set of axes, do the same for diastolic blood pressure.
tiledlayout(1,2) % Left axes ax1 = nexttile; boxchart(ax1,Systolic,'GroupByColor',Smoker) ylabel(ax1,'Systolic Blood Pressure') legend % Right axes ax2 = nexttile; boxchart(ax2,Diastolic,'GroupByColor',Smoker) ylabel(ax2,'Diastolic Blood Pressure') legend
Update Color of BoxChart
Object
Create a set of colorcoded box charts, returned as a vector of BoxChart
objects. Use the vector to change the color of one box chart.
Load the patients
data set. Convert Gender
and Smoker
to categorical
variables. Specify the descriptive category names Smoker
and Nonsmoker
rather than 1
and 0
.
load patients Gender = categorical(Gender); Smoker = categorical(Smoker,logical([1 0]),{'Smoker','Nonsmoker'});
Combine the Gender
and Smoker
variables into one grouping variable cgroupdata
. Create box charts showing the distribution of diastolic blood pressure levels for each pairing of gender and smoking status. b
is a vector of BoxChart
objects, one for each group of data.
cgroupdata = Gender.*Smoker;
b = boxchart(Diastolic,'GroupByColor',cgroupdata)
b = 4x1 BoxChart array: BoxChart BoxChart BoxChart BoxChart
legend('Location','southeast')
Update the color of the third box chart by using the SeriesIndex
property. Updating the SeriesIndex
property changes both the box face color and the outlier marker color.
b(3).SeriesIndex = 6;
Visualize and Find Outliers
Create a box chart from power outage data with many outliers, and make it easier to distinguish them visually by changing the properties of the BoxChart
object. Find the indices for the outlier entries.
Read power outage data into the workspace as a table. Display the first few rows of the table.
outages = readtable('outages.csv');
head(outages)
ans=8×6 table
Region OutageTime Loss Customers RestorationTime Cause
_____________ ________________ ______ __________ ________________ ___________________
{'SouthWest'} 20020201 12:18 458.98 1.8202e+06 20020207 16:50 {'winter storm' }
{'SouthEast'} 20030123 00:49 530.14 2.1204e+05 NaT {'winter storm' }
{'SouthEast'} 20030207 21:15 289.4 1.4294e+05 20030217 08:14 {'winter storm' }
{'West' } 20040406 05:44 434.81 3.4037e+05 20040406 06:10 {'equipment fault'}
{'MidWest' } 20020316 06:18 186.44 2.1275e+05 20020318 23:23 {'severe storm' }
{'West' } 20030618 02:49 0 0 20030618 10:54 {'attack' }
{'West' } 20040620 14:39 231.29 NaN 20040620 19:16 {'equipment fault'}
{'West' } 20020606 19:28 311.86 NaN 20020607 00:51 {'equipment fault'}
Create a BoxChart
object b
from the outages.Customers
values, which indicate how many customers were affected by each power outage. boxchart
discards entries with NaN
values.
b = boxchart(outages.Customers);
ylabel('Number of Customers')
The plot contains many outliers. To better see them, jitter the outliers and change the outlier marker style. When you set the JitterOutliers
property of the BoxChart
object to 'on'
, the software randomly displaces the outlier markers horizontally so that they are unlikely to overlap perfectly. The values and vertical positions of the outliers are unchanged.
b.JitterOutliers = 'on'; b.MarkerStyle = '.';
You can now more easily see the distribution of outliers.
To find the outlier indices, use the isoutlier
function. Specify the 'quartiles'
method of computing outliers to match the boxchart
outlier definition. Use the indices to create the outliers
table, which contains a subset of the outages
data. Notice that isoutlier
identifies 96 outliers.
idx = isoutlier(outages.Customers,'quartiles');
outliers = outages(idx,:);
size(outliers,1)
ans = 96
Because of all the outliers, the quartiles of the box chart are hard to see. To inspect them, change the yaxis limits.
ylim([0 4e5])
Input Arguments
ydata
— Sample data
numeric vector  numeric matrix
Sample data, specified as a numeric vector or matrix.
If
ydata
is a matrix, thenboxchart
creates a box chart for each column ofydata
.If
ydata
is a vector and you do not specifyxgroupdata
orcgroupdata
, thenboxchart
creates a single box chart.If
ydata
is a vector and you do specifyxgroupdata
orcgroupdata
, thenboxchart
creates a box chart for each unique value combination inxgroupdata
andcgroupdata
.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
xgroupdata
— Positional grouping variable
numeric vector  categorical vector
Positional grouping variable, specified as a numeric or categorical vector.
xgroupdata
must have the same length as the vector
ydata
; you cannot specify xgroupdata
when
ydata
is a matrix.
boxchart
groups the data in ydata
according to the unique value combinations in xgroupdata
and
cgroupdata
. The function creates a box chart for each group of
data and positions each box chart at the corresponding xgroupdata
value. By default, boxchart
vertically orients the box charts and
displays the xgroupdata
values along the
xaxis. You can change the box chart orientation by using the
Orientation
property.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 categorical
cgroupdata
— Color grouping variable
numeric vector  categorical vector  logical vector  string array  character vector  cell array of character vectors
Color grouping variable, specified as a numeric vector, categorical vector, logical
vector, string array, character vector, or cell array of character vectors.
cgroupdata
must have the same length as the vector
ydata
; you cannot specify cgroupdata
when
ydata
is a matrix.
boxchart
groups the data in ydata
according to the unique value combinations in xgroupdata
and
cgroupdata
. The function creates a box chart for each group of
data and assigns the same color to groups with the same cgroupdata
value.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 categorical
 logical
 string
 char
 cell
ax
— Target axes
Axes
object
Target axes, specified as an Axes
object. If you do not specify the
axes, then boxchart
uses the current axes
(gca
).
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: boxchart([rand(10,4); 4*rand(1,4)],'BoxFaceColor',[0 0.5
0],'MarkerColor',[0 0.5 0])
creates box charts with green boxes and green
outliers, if applicable.
The BoxChart
properties listed here are only a subset. For a complete
list, see BoxChart Properties.
BoxFaceColor
— Box color
RGB triplet  hexadecimal color code  color name  short name
Box color, specified as an RGB triplet, hexadecimal color code, color name, or short name.
For a custom color, specify an RGB triplet or a hexadecimal color code.
An RGB triplet is a threeelement row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range
[0,1]
; for example,[0.4 0.6 0.7]
.A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (
#
) followed by three or six hexadecimal digits, which can range from0
toF
. The values are not case sensitive. Thus, the color codes'#FF8800'
,'#ff8800'
,'#F80'
, and'#f80'
are equivalent.
Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.
Color Name  Short Name  RGB Triplet  Hexadecimal Color Code  Appearance 

'red'  'r'  [1 0 0]  '#FF0000'  
'green'  'g'  [0 1 0]  '#00FF00'  
'blue'  'b'  [0 0 1]  '#0000FF'  
'cyan'
 'c'  [0 1 1]  '#00FFFF'  
'magenta'  'm'  [1 0 1]  '#FF00FF'  
'yellow'  'y'  [1 1 0]  '#FFFF00'  
'black'  'k'  [0 0 0]  '#000000'  
'white'  'w'  [1 1 1]  '#FFFFFF'  
'none'  Not applicable  Not applicable  Not applicable  No color 
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB^{®} uses in many types of plots.
RGB Triplet  Hexadecimal Color Code  Appearance 

[0 0.4470 0.7410]  '#0072BD'  
[0.8500 0.3250 0.0980]  '#D95319'  
[0.9290 0.6940 0.1250]  '#EDB120'  
[0.4940 0.1840 0.5560]  '#7E2F8E'  
[0.4660 0.6740 0.1880]  '#77AC30'  
[0.3010 0.7450 0.9330]  '#4DBEEE'  
[0.6350 0.0780 0.1840]  '#A2142F' 
Example: b =
boxchart(rand(10,1),'BoxFaceColor','red')
Example: b.BoxFaceColor = [0 0.5 0.5];
Example: b.BoxFaceColor = '#EDB120';
MarkerStyle
— Outlier style
'o'
(default)  '+'
 '*'
 '.'
 'x'
 ...
Outlier style, specified as one of the options listed in this table.
Marker  Description  Resulting Marker 

'o'  Circle 

'+'  Plus sign 

'*'  Asterisk 

'.'  Point 

'x'  Cross 

'_'  Horizontal line 

''  Vertical line 

's'  Square 

'd'  Diamond 

'^'  Upwardpointing triangle 

'v'  Downwardpointing triangle 

'>'  Rightpointing triangle 

'<'  Leftpointing triangle 

'p'  Pentagram 

'h'  Hexagram 

'none'  No markers  Not applicable 
Example: b = boxchart([rand(10,1);2],'MarkerStyle','x')
Example: b.MarkerStyle = 'x';
JitterOutliers
— Outlier marker displacement
'off'
(default)  on/off logical value
Outlier marker displacement, specified as 'on'
or 'off'
, or as numeric or logical 1
(true
) or 0
(false
). A value of 'on'
is equivalent to true
, and 'off'
is equivalent to false
. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState
.
If you set the JitterOutliers
property to
'on'
, then boxchart
randomly displaces the
outlier markers along the XData
direction to help you distinguish
between outliers that have similar ydata
values. For an example,
see Visualize and Find Outliers.
Example: b = boxchart([rand(20,1);2;2;2],'JitterOutliers','on')
Example: b.JitterOutliers = 'on';
Notch
— Median comparison display
'off'
(default)  on/off logical value
Median comparison display, specified as 'on'
or 'off'
, or as numeric or logical 1
(true
) or 0
(false
). A value of 'on'
is equivalent to true
, and 'off'
is equivalent to false
. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState
.
If you set the Notch
property to 'on'
, then
boxchart
creates a tapered, shaded region around each median.
Box charts whose notches do not overlap have different medians at the 5% significance
level. For more information, see Box Chart (Box Plot).
Notches can extend beyond the lower and upper quartiles.
Example: b = boxchart(rand(10,2),'Notch','on')
Example: b.Notch = 'on';
Orientation
— Orientation of box charts
'vertical'
(default)  'horizontal'
Orientation of box charts, specified as 'vertical'
or
'horizontal'
. By default, the box charts are vertically
orientated, so that the ydata
statistics are aligned with the
yaxis. Regardless of the orientation,
boxchart
stores the ydata
values in the
YData
property of the BoxChart
object.
Example: b = boxchart(rand(10,1),'Orientation','horizontal')
Example: b.Orientation = 'horizontal';
Output Arguments
b
— Box charts
vector of BoxChart
objects
Box charts, returned as a vector of BoxChart
objects.
b
contains one BoxChart
object for each unique
value in cgroupdata
. For more information, see BoxChart Properties.
More About
Box Chart (Box Plot)
A box chart, or box plot, provides a visual representation of summary statistics for a data sample. Given numeric data, the corresponding box chart displays the following information: the median, the lower and upper quartiles, any outliers (computed using the interquartile range), and the minimum and maximum values that are not outliers.
The line inside of each box is the sample median. You can compute the value of the median using the
median
function.The top and bottom edges of each box are the upper and lower quartiles, respectively. The distance between the top and bottom edges is the interquartile range (IQR).
For more information on how the quartiles are computed, see
quantile
, where the upper quartile corresponds to the 0.75 quantile and the lower quartile corresponds to the 0.25 quantile.Outliers are values that are more than 1.5 · IQR away from the top or bottom of the box. By default,
boxchart
displays each outlier using an'o'
symbol. The outlier computation is comparable to that of theisoutlier
function with the'quartiles'
method.The whiskers are lines that extend above and below each box. One whisker connects the upper quartile to the nonoutlier maximum (the maximum value that is not an outlier), and the other connects the lower quartile to the nonoutlier minimum (the minimum value that is not an outlier).
Notches help you compare sample medians across multiple box charts. When you specify
'Notch','on'
, theboxchart
function creates a tapered, shaded region around each median. Box charts whose notches do not overlap have different medians at the 5% significance level. The significance level is based on a normal distribution assumption, but the median comparison is reasonably robust for other distributions.The top and bottom edges of the notch region correspond to $$m+\left(1.57\cdot IQR\right)/\sqrt{n}$$ and $$m\left(1.57\cdot IQR\right)/\sqrt{n}$$, respectively, where m is the median, IQR is the interquartile range, and n is the number of data points, excluding
NaN
values.
Tips
Use data tips to explore the data in
BoxChart
objects. Some options are not available in the Live Editor.You can add two types of data tips to a
BoxChart
object: one for each box chart and one for each outlier. A general data tip appears at the nonoutlier maximum value, regardless of where you click on the box chart.Note
The displayed
Num Points
value includesNaN
values in the correspondingydata
, butboxchart
discards theNaN
values before computing the box chart statistics.You can use the
datatip
function to add more data tips to aBoxChart
object, but the indexing of data tips differs from other charts.boxchart
first assigns indices to the box charts and then assigns indices to the outliers. For example, if aBoxChart
objectb
displays two box charts and one outlier,datatip(b,'DataIndex',3)
creates a data tip at the outlier point.
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