Given quartiles, how do I draw a box-whisker using MATLAB, matplotlib, gnuplot, or some other pac...

Drawing Box-Whisker Plots from Quartiles in MATLAB, Matplotlib, and Gnuplot

Learn how to visualize data distribution using box-whisker plots when you only have quartile values, with practical examples in MATLAB, Matplotlib (Python), and Gnuplot.

Box-whisker plots, also known as box plots, are powerful tools for visualizing the distribution of a dataset. They display the five-number summary of a set of data: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. While many plotting libraries can generate these plots directly from raw data, it's often necessary to create them when you only have the pre-calculated quartile values. This article will guide you through generating box-whisker plots using MATLAB, Matplotlib, and Gnuplot, focusing on scenarios where you provide the quartile statistics rather than raw data.

Understanding the Five-Number Summary

Before diving into the plotting, let's quickly review the components of a box-whisker plot. The 'box' typically spans from the first quartile (Q1) to the third quartile (Q3), representing the interquartile range (IQR). A line inside the box marks the median (Q2). The 'whiskers' extend from the box to the minimum and maximum values within a certain range, often 1.5 times the IQR from the quartiles. Any data points outside the whiskers are considered outliers and are plotted individually. When you have pre-calculated quartiles, you're essentially providing these summary statistics directly to the plotting function or script.

flowchart TD
    A[Raw Data] --> B{Calculate Quartiles}
    B --> C[Minimum]
    B --> D["First Quartile (Q1)"]
    B --> E["Median (Q2)"]
    B --> F["Third Quartile (Q3)"]
    B --> G[Maximum]
    C & D & E & F & G --> H["Plot Box-Whisker (from Quartiles)"]

Process of generating a box-whisker plot from raw data to quartile-based plotting.

MATLAB: Plotting with boxplot and plot

MATLAB's boxplot function is primarily designed for raw data. However, you can simulate a box plot from quartiles by carefully constructing a dataset or by using lower-level plotting functions. A common workaround involves creating a dummy dataset that yields the desired quartiles, or more directly, using plot to draw the box and whiskers manually. For simplicity and directness, we'll focus on a method that leverages boxplot with a synthetic dataset or a more manual approach if boxplot is too restrictive.

% Define your quartile values
min_val = 10;
q1 = 15;
median_val = 20;
q3 = 25;
max_val = 30;

% Create a dummy dataset that will produce these quartiles
% This is a simplified approach and might not perfectly replicate all boxplot features
% For a more robust solution, you might need to draw elements manually.

% A simple way to get boxplot to draw from summary stats is to create a vector
% that has these values as its min, Q1, median, Q3, max.
% This is an approximation. For precise control, manual drawing is better.

data = [min_val, q1, median_val, q3, max_val];

figure;
boxplot(data, 'Labels', {'My Data'});

title('Box-Whisker Plot from Quartiles (MATLAB)');
ylabel('Value');

% --- More manual approach for precise control ---
figure;
hold on;

% Draw the box
rectangle('Position', [0.75, q1, 0.5, q3-q1], 'EdgeColor', 'k', 'FaceColor', [0.8 0.8 0.8]);

% Draw the median line
plot([0.75, 1.25], [median_val, median_val], 'k-', 'LineWidth', 2);

% Draw whiskers
plot([1, 1], [min_val, q1], 'k-'); % Lower whisker
plot([1, 1], [q3, max_val], 'k-'); % Upper whisker

% Draw whisker caps
plot([0.9, 1.1], [min_val, min_val], 'k-');
plot([0.9, 1.1], [max_val, max_val], 'k-');

set(gca, 'XTick', 1, 'XTickLabel', {'Custom Data'});
xlim([0.5, 1.5]);
y_range = max_val - min_val;
ylim([min_val - 0.1*y_range, max_val + 0.1*y_range]);

title('Manual Box-Whisker Plot from Quartiles (MATLAB)');
ylabel('Value');
hold off;

MATLAB code for generating a box-whisker plot from pre-defined quartile values. The manual approach offers more control.

Matplotlib (Python): boxplot with positions and widths

Matplotlib's boxplot function is highly flexible. While it typically takes raw data, you can provide pre-calculated statistics by creating a dummy dataset that, when processed by boxplot, will result in your desired quartiles. A more direct approach for plotting pre-calculated statistics is not natively supported by boxplot in the same way as raw data, but you can achieve the visual representation by manually drawing the components or by feeding a specially crafted dataset. However, a common and effective workaround is to use matplotlib.pyplot.boxplot with a single data point for each box, and then manually adjust the box and whisker properties if needed, or to use a library like seaborn which can sometimes accept summary statistics more directly.

import matplotlib.pyplot as plt
import numpy as np

# Define your quartile values
min_val = 10
q1 = 15
median_val = 20
q3 = 25
max_val = 30

# Matplotlib's boxplot function expects raw data.
# To plot from quartiles, we can create a dummy dataset
# or manually draw the components.

# Method 1: Manual drawing (more control)
fig, ax = plt.subplots()

# Box (Q1 to Q3)
box_height = q3 - q1
ax.add_patch(plt.Rectangle([0.75, q1], 0.5, box_height, facecolor='lightgray', edgecolor='black'))

# Median line
ax.plot([0.75, 1.25], [median_val, median_val], color='black', linewidth=2)

# Whiskers
ax.plot([1, 1], [min_val, q1], color='black', linestyle='-') # Lower whisker
ax.plot([1, 1], [q3, max_val], color='black', linestyle='-') # Upper whisker

# Whisker caps
ax.plot([0.9, 1.1], [min_val, min_val], color='black', linestyle='-')
ax.plot([0.9, 1.1], [max_val, max_val], color='black', linestyle='-')

ax.set_xticks([1])
ax.set_xticklabels(['Custom Data'])
ax.set_ylabel('Value')
ax.set_title('Manual Box-Whisker Plot from Quartiles (Matplotlib)')

plt.show()

# Method 2: Using boxplot with a 'fake' dataset (less precise for exact quartile control)
# This method is generally for when you have raw data. 
# If you only have quartiles, manual drawing is often clearer.
# For demonstration, if you had a dataset that *resulted* in these quartiles:
# data_for_boxplot = np.array([min_val, q1, median_val, q3, max_val]) 
# plt.figure()
# plt.boxplot(data_for_boxplot, labels=['My Data'])
# plt.title('Box-Whisker Plot from Quartiles (Matplotlib - Approx)')
# plt.ylabel('Value')
# plt.show()

Python Matplotlib code for drawing a box-whisker plot using pre-calculated quartile values by manually constructing the plot elements.

Gnuplot: candlesticks and boxerrorbars

Gnuplot is a powerful command-line driven plotting utility. It offers specific plotting styles that are well-suited for creating box-whisker plots from summary statistics. The candlesticks and boxerrorbars plotting styles are particularly useful here, as they allow you to specify the five-number summary directly from data columns. You'll typically prepare your quartile data in a text file, and then instruct Gnuplot to read these columns for plotting.

# Create a data file named 'quartiles.dat' with the following content:
# Index Min Q1 Median Q3 Max
# 1     10  15 20     25 30

# Gnuplot script
set terminal pngcairo enhanced font 'arial,10' size 800,600
set output 'boxplot_gnuplot.png'

set style fill solid 0.5 border -1
set boxwidth 0.5

set ylabel 'Value'
set title 'Box-Whisker Plot from Quartiles (Gnuplot)'

# Plotting using candlesticks style
# The columns are: x, open, low, high, close
# For boxplot, we map: x, Q1, Min, Max, Q3
# The median is plotted separately.

plot 'quartiles.dat' using 1:3:2:5:4 with candlesticks title 'Box' fs transparent solid 0.3 noborder, \
     '' using 1:4:4:4:4 with candlesticks lt -1 lw 2 title 'Median' 

# Alternative using boxerrorbars (requires more manual drawing for median)
# plot 'quartiles.dat' using 1:4:2:5 with boxerrorbars title 'Box and Whiskers', \
#      '' using 1:4:4:4:4 with points pt 7 ps 1 title 'Median'

Gnuplot script to generate a box-whisker plot from a data file containing quartile values. The candlesticks style is adapted for this purpose.

Choosing the Right Tool

The best tool depends on your existing environment and specific needs. MATLAB is excellent for engineering and scientific computing, offering integrated environments. Matplotlib, being part of the Python ecosystem, is highly versatile and popular for general-purpose data visualization and scripting. Gnuplot is a lightweight, powerful tool for generating high-quality plots from the command line, ideal for automated plotting in scripts or when resources are limited. All three can effectively create box-whisker plots from pre-calculated quartiles, though the implementation details vary.

MATLAB

% Example data for multiple box plots min_vals = [10, 12, 8]; q1_vals = [15, 16, 10]; median_vals = [20, 22, 14]; q3_vals = [25, 28, 18]; max_vals = [30, 35, 22];

num_boxes = length(min_vals);

figure; hold on;

for i = 1:num_boxes x_pos = i;

% Draw the box
rectangle('Position', [x_pos - 0.25, q1_vals(i), 0.5, q3_vals(i)-q1_vals(i)], 'EdgeColor', 'k', 'FaceColor', [0.8 0.8 0.8]);

% Draw the median line
plot([x_pos - 0.25, x_pos + 0.25], [median_vals(i), median_vals(i)], 'k-', 'LineWidth', 2);

% Draw whiskers
plot([x_pos, x_pos], [min_vals(i), q1_vals(i)], 'k-'); % Lower whisker
plot([x_pos, x_pos], [q3_vals(i), max_vals(i)], 'k-'); % Upper whisker

% Draw whisker caps
plot([x_pos - 0.1, x_pos + 0.1], [min_vals(i), min_vals(i)], 'k-');
plot([x_pos - 0.1, x_pos + 0.1], [max_vals(i), max_vals(i)], 'k-');

end

set(gca, 'XTick', 1:num_boxes, 'XTickLabel', {'Group A', 'Group B', 'Group C'}); xlim([0.5, num_boxes + 0.5]); y_min = min(min_vals) - 0.1 * (max(max_vals) - min(min_vals)); y_max = max(max_vals) + 0.1 * (max(max_vals) - min(min_vals)); ylim([y_min, y_max]);

title('Multiple Box-Whisker Plots (MATLAB)'); ylabel('Value'); hold off;

Python (Matplotlib)

import matplotlib.pyplot as plt import numpy as np

Example data for multiple box plots

min_vals = [10, 12, 8] q1_vals = [15, 16, 10] median_vals = [20, 22, 14] q3_vals = [25, 28, 18] max_vals = [30, 35, 22]

num_boxes = len(min_vals)

fig, ax = plt.subplots()

for i in range(num_boxes): x_pos = i + 1

# Box (Q1 to Q3)
box_height = q3_vals[i] - q1_vals[i]
ax.add_patch(plt.Rectangle([x_pos - 0.25, q1_vals[i]], 0.5, box_height, facecolor='lightgray', edgecolor='black'))

# Median line
ax.plot([x_pos - 0.25, x_pos + 0.25], [median_vals[i], median_vals[i]], color='black', linewidth=2)

# Whiskers
ax.plot([x_pos, x_pos], [min_vals[i], q1_vals[i]], color='black', linestyle='-') # Lower whisker
ax.plot([x_pos, x_pos], [q3_vals[i], max_vals[i]], color='black', linestyle='-') # Upper whisker

# Whisker caps
ax.plot([x_pos - 0.1, x_pos + 0.1], [min_vals[i], min_vals[i]], color='black', linestyle='-')
ax.plot([x_pos - 0.1, x_pos + 0.1], [max_vals[i], max_vals[i]], color='black', linestyle='-')

ax.set_xticks(range(1, num_boxes + 1)) ax.set_xticklabels(['Group A', 'Group B', 'Group C']) ax.set_ylabel('Value') ax.set_title('Multiple Box-Whisker Plots (Matplotlib)')

plt.show()

Gnuplot

Create a data file named 'multiple_quartiles.dat' with the following content:

Index Min Q1 Median Q3 Max

1 10 15 20 25 30

2 12 16 22 28 35

3 8 10 14 18 22

Gnuplot script for multiple box plots

set terminal pngcairo enhanced font 'arial,10' size 800,600 set output 'multiple_boxplot_gnuplot.png'

set style fill solid 0.5 border -1 set boxwidth 0.5

set ylabel 'Value' set title 'Multiple Box-Whisker Plots from Quartiles (Gnuplot)'

set xtics ('Group A' 1, 'Group B' 2, 'Group C' 3) set xrange [0.5:3.5]

plot 'multiple_quartiles.dat' using 1:3:2:5:4 with candlesticks title 'Box' fs transparent solid 0.3 noborder,
'' using 1:4:4:4:4 with candlesticks lt -1 lw 2 title 'Median'