generates a plot of quantiles of list against the quantiles of a normal distribution.


generates a plot of quantiles of the distribution dist against the quantiles of a normal distribution.


generates a plot of the quantiles of data against the quantiles of rdata.


generates a plot of the quantiles of data against the quantiles of a symbolic distribution rdist.


generates a plot of quantiles of datai against the quantiles of a reference distribution ref.

Details and Options


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Basic Examples  (5)

Compare data to a normal distribution:

Compare data to a specific distribution:

Compare data to an estimated distribution:

Compare two datasets:

Compare several datasets and include a legend:

Scope  (22)

Data and Distributions  (11)

QuantilePlot works with numeric data:

QuantilePlot works with symbolic distributions:

Use multiple datasets and distributions:

The default reference distribution is the closest estimated NormalDistribution:

Specify data or distributions as the reference:

Reference distributions are estimated for each dataset:

Estimate specific reference distributions for numeric datasets:

Use all forms of built-in distributions:




Use all forms of data.

Numeric values in an association are used as the coordinates:

Numeric keys and values in an association are used as the and coordinates:

Plot time series directly:

The weights in WeightedData are ignored:

Presentation  (11)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Include legends for each dataset:

Add labels:

Use specific styles for the reference line:

Turn off the reference line:

Provide an interactive Tooltip for the data:

Provide a specific tooltip for the data:

Create filled plots:

Use shapes to distinguish different datasets:

Use Joined to connect datasets with lines:

Use a plot theme:

Options  (75)

AspectRatio  (1)

Choose the ratio of height to width from the actual plot values:

Axes  (1)

Draw axes instead of a frame:

AxesLabel  (1)

Use labels based on variables specified:

ClippingStyle  (4)

Omit clipped regions of the plot:

Show the clipped regions like the rest of the curve:

Show the clipped regions with red lines:

Show the clipped regions as red and thick:

ColorFunction  (6)

ColorFunction requires at least one dataset to be Joined:

Color by scaled and coordinates:

Color with a named color scheme:

Fill to the reference line with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use Automatic in MeshShading to use ColorFunction:

ColorFunctionScaling  (2)

Color the line based on scaled value:

Color the line based on unscaled value:

Filling  (7)

Fill from data to the reference line:

Use symbolic or explicit values for filling:

Points fill with stems:

Curves fill with solid regions:

Fill from the third dataset to the axis:

Fill between datasets using a particular style:

Use different styles above and below the filling level:

Filling only applies where the datasets overlap:

FillingStyle  (3)

Use different fill colors:

Fill with transparent orange regions:

Use blue above the fill level and red below:

Joined  (2)

Datasets are not joined by default:

Join the points:

Symbolic distributions are joined by default:

Mesh  (4)

Use 20 mesh levels evenly spaced in the direction:

Use the mesh to divide the curve into deciles:

Use an explicit list of values for the mesh in the direction:

Specify Style and mesh levels in the direction:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show five mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling the curve:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

MeshStyle  (4)

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big red mesh points in the direction:

Method  (4)

By default, the reference line is drawn through the first and third quartiles of data:

Draw the best-fit line through data:

The reference line represents the reference distribution:

Draw a diagonal reference line:

PlotLegends  (7)

By default, no legends are used:

Generate a legend using labels:

Generate a legend using placeholders:

Legends use the same styles as the plot:

Use Placed to specify the legend placement:

Place the legend inside the plot:

Use LineLegend to change the legend appearance:

PlotMarkers  (7)

QuantilePlot normally uses distinct colors to distinguish different sets of data:

Use colors and shapes to distinguish sets of data:

Use shapes only:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

PlotRange  (3)

PlotRange is automatically calculated:

Show the whole dataset:

Show the distribution for between 1 and 2 and between -1 and 3:

PlotStyle  (3)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotTheme  (2)

Use a theme with simple ticks and grid lines in a high contrast color scheme:

Change the color scheme:

ReferenceLineStyle  (4)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

Draw a red dotted reference line:

Draw a solid red reference line:

Use None to turn off the reference line:

ReferenceLineStyle can be combined with PlotStyle:

ScalingFunctions  (2)

Data is normally shown on linear scales:

Plot the data on a log-scaled axis:

Applications  (5)

Visually test whether data was drawn from a particular distribution:

Linearity occurs when the data was drawn from the reference distribution:

Deviations from linearity occur when the data was not drawn from the reference distribution:

The residuals resulting from a LinearModelFit should be normally distributed. Here, some data is simulated with normal and exponential noise of equal variance:

Fit linear models to the simulated data:

There is strong visual evidence that the residuals are not normal in the first model:

DistributionFitTest can be used to make a quantitative statement about normality:

The heights of singers from the New York Choral Society were recorded along with the voice part of each singer. Voice parts, in increasing order of pitch, include bass, tenor, alto, and soprano:

The mean heights for each voice part:

Plotting the height quantiles of Soprano 1 against the other voice parts suggests that there is an additive shift in height with a voice part:

Rainfall, in acre-feet, was recorded from 52 clouds, of which 26 were chosen randomly and seeded with silver oxide:

Clearly, the seeded clouds produce more rain than the control:

A log-log scaled plot suggests that the increase is about one order of magnitude:

Compare two time slices for a random process:

Properties & Relations  (9)

With no second argument, data is compared against an estimated normal distribution:

Comparing with UniformDistribution[{0,1}] is equivalent to plotting the quantile:

ProbabilityPlot compares CDF values for the data.

ProbabilityScalePlot scales the axes so that points from distributions are on a straight line:

BoxWhiskerChart and DistributionChart can be used to visualize the distribution of data:

SmoothHistogram and Histogram can be used to visualize the distribution of data:

DiscretePlot can be used to visualize the discrete distributions:

Use ListPlot to see the data:

QuantilePlot ignores time stamps when input is a TimeSeries:

Wolfram Research (2010), QuantilePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantilePlot.html (updated 2014).


Wolfram Research (2010), QuantilePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantilePlot.html (updated 2014).


Wolfram Language. 2010. "QuantilePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/QuantilePlot.html.


Wolfram Language. (2010). QuantilePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuantilePlot.html


@misc{reference.wolfram_2022_quantileplot, author="Wolfram Research", title="{QuantilePlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/QuantilePlot.html}", note=[Accessed: 29-May-2023 ]}


@online{reference.wolfram_2022_quantileplot, organization={Wolfram Research}, title={QuantilePlot}, year={2014}, url={https://reference.wolfram.com/language/ref/QuantilePlot.html}, note=[Accessed: 29-May-2023 ]}