Plotting Data

When plotting data, you often need to show uncertainties or mark important reference values. Matplotlib provides specific functions for these common tasks.

Error Bars

Experimental measurements have associated uncertainties. You can display these using error bars.

import numpy as np
import matplotlib.pyplot as plt
%config InlineBackend.figure_format='retina'

# Absorbance measurements with uncertainties
concentration = np.array([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
absorbance = np.array([0.00, 0.18, 0.39, 0.58, 0.81, 0.99])
uncertainty = np.array([0.02, 0.03, 0.02, 0.04, 0.03, 0.02])

plt.errorbar(concentration, absorbance, yerr=uncertainty, fmt='o')
plt.xlabel('Concentration / mM')
plt.ylabel('Absorbance')
plt.show()

The plt.errorbar() function takes three main arguments:

• The x-values

• The y-values

• yerr: the uncertainties in the y-direction

The fmt parameter specifies the format of the data points (same as in plt.plot()).

You can combine error bars with connecting lines:

plt.errorbar(concentration, absorbance, yerr=uncertainty, fmt='o-')
plt.xlabel('Concentration / mM')
plt.ylabel('Absorbance')
plt.show()

For uncertainties in the x-direction, use the xerr parameter. You can also have uncertainties in both directions:

time = np.array([0, 5, 10, 15, 20, 25])
temperature = np.array([20.0, 24.5, 31.2, 39.8, 50.1, 62.5])
time_uncertainty = np.array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5])
temp_uncertainty = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.8])

plt.errorbar(time, temperature, xerr=time_uncertainty, yerr=temp_uncertainty, fmt='o')
plt.xlabel('Time / min')
plt.ylabel('Temperature / °C')
plt.show()

Reference Lines

It is often useful to mark specific values on your plots, such as theoretical predictions, equivalence points, or threshold values.

# pH titration curve
volume = np.linspace(0, 30, 100)
pH = 3 + 8 / (1 + np.exp(-(volume - 15)))

plt.plot(volume, pH)
plt.axhline(y=7, color='gray', linestyle='--', label='Neutral pH')
plt.axvline(x=15, color='red', linestyle='--', label='Equivalence point')
plt.xlabel('Volume of NaOH / mL')
plt.ylabel('pH')
plt.legend()
plt.show()

• plt.axhline(y=value) draws a horizontal line at the specified y-value

• plt.axvline(x=value) draws a vertical line at the specified x-value

These lines extend across the entire axis by default. You can customise their appearance using the same parameters as plt.plot() (colour, line style, etc.).

Exercise

You performed a Beer-Lambert law calibration experiment, measuring absorbance at different concentrations:

Concentration (mM)	Absorbance	Uncertainty
0.0	0.00	0.01
0.5	0.12	0.02
1.0	0.24	0.02
1.5	0.35	0.03
2.0	0.48	0.02
2.5	0.59	0.03

Create a plot that:

1. Shows the data points with error bars

2. Connects the points with a line

3. Includes a horizontal reference line at absorbance = 0.36 (an unknown sample you measured)

4. Has appropriate axis labels

5. Includes a legend

Show solution

concentration = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5])
absorbance = np.array([0.00, 0.12, 0.24, 0.35, 0.48, 0.59])
uncertainty = np.array([0.01, 0.02, 0.02, 0.03, 0.02, 0.03])

plt.errorbar(concentration, absorbance, yerr=uncertainty, fmt='o-', label='Calibration')
plt.axhline(y=0.36, color='red', linestyle='--', label='Unknown sample')
plt.xlabel('Concentration / mM')
plt.ylabel('Absorbance')
plt.legend()
plt.show()

Summary

You have learned how to:

• Display measurement uncertainties using plt.errorbar()

• Add error bars in the x-direction with xerr and y-direction with yerr

• Mark reference values with plt.axhline() and plt.axvline()

• Combine error bars with connecting lines and reference markers