The boxplot functionlity is rather rigid, in that you cannot in a single call set different whisker sizes for each box. You need multiple calls to the box plot function, plotting to the same axes. I recently wrote a function for this:
function [fig, ax] = box_plots_with_differing_whiskers_fn( ...
data_cells, ...
outlier_limits, ...
x_tick_labels, ...
x_label, ...
y_label ...
)
%
% box_plots_with_differing_whiskers_fn
%
% Generates a figure–axes pair that contains a series of box plots with
% whiskers of differing sizes.
%
% NOTE: boxplot draws points as outliers if they are greater than q3 + w ×
% (q3 – q1) or less than q1 – w × (q3 – q1), where w is the multiplier
% Whisker, and q1 and q3 are the 25th and 75th percentiles of the sample
% data, respectively.
%
arguments
data_cells (:,1) cell
outlier_limits (:,1) double
x_tick_labels (:,1) string
x_label (1,1) string
y_label (1,1) string
end % arguments
assert ( numel( data_cells ) == numel ( outlier_limits ), "There need to be as many data cells as there are outlier limits" );
assert ( numel( data_cells ) == numel ( x_tick_labels ), "There need to be as many data cells as there are x-tick labels." );
% Create figure and places axes in it.
fig = figure();
ax = axes(fig);
xlabel(x_label, "Interpreter", "latex");
ylabel(y_label, "Interpreter", "latex");
% Add box plots to the same axes.
hold on
index_range = 1 : numel(data_cells);
for ii = index_range
% Compute upper whisker size based on the algorithm given in box plot
% documentation.
q1 = quantile(data_cells{ii}, 0.25);
q3 = quantile(data_cells{ii}, 0.75);
ol = outlier_limits(ii);
upper_whisker = ( ol - q3 ) / ( q3 - q1 ) ;
% Add box plot to axes.
bp = boxplot( ...
ax, ...
data_cells{ii}, ...
"Positions", ii, ...
"Whisker", upper_whisker ...
) ;
end % for
xticks(ax, index_range) ;
xticklabels(ax, x_tick_labels) ;
grid on
hold off
end % function
Note that more code should be added, to make it possible to adjust the lower whiskers and so forth. There might also be unhandled error cases, such as not checking that the whisker values are above each 75 % quantile.
