import numpy as np
from matplotlib import pyplot as plt

N = 1000;

r_noise = np.random.uniform(-0.01,0.01,size=(1,N))
theta_noise = np.random.uniform(-0.35,0.35,size=(1,N))
r = 1 + r_noise;
theta = np.pi/2 + theta_noise;
x = r * np.cos(theta);
y = r * np.sin(theta);

x_meanNon = np.mean(x);
y_meanNon = np.mean(y);

x_meanLin = 0.0;
y_meanLin = 1.0;

fig = plt.figure(linewidth=2)
plt.plot(x[:],y[:], 'c.')
plt.plot(x_meanNon ,y_meanNon , 'ro')
plt.plot(x_meanLin ,y_meanLin , 'bo')
plt.text(x_meanNon ,y_meanNon , 'Nonlinear Mean')
plt.text(x_meanLin ,y_meanLin , 'Linearized Mean')
plt.xlabel("X")
plt.ylabel("Y")
plt.show()