matplotlib scatter with geometric standard deviations

plt.scatter(xlist, ylist)

plt.errorbar(x_ave, y_ave, yerr=1, xerr=1, fmt='*', color='red', ecolor='black', ms=20, 
             elinewidth=4, capsize=10, capthick=4, label='Average')

handles, labels = ax.get_legend_handles_labels()
handles = [h[0] for h in handles]
ax.legend(handles, labels, loc='best', fontsize=16)

pylab_examples example code: errorbar_demo.py

sphx-glr-gallery-lines-bars-and-markers-errorbar-limits-simple

plt.errorbar(x, y, yerr=dy, fmt='o', color='black',
ecolor='lightgray', elinewidth=3, capsize=0);

image.png