The Normal (Gaussian) distribution is defined by two numbers: mean μ (center) and variance σ² (spread). It's the most important distribution in neuroscience.

68% of data falls within 1σ of the mean 95% within 2σ, 99.7% within 3σ

The 68-95-99.7 rule — memorize this!

import numpy as np

# Simulate noisy neuron firing rates
mean_rate = 20.0   # Hz
std_dev   = 5.0    # Hz
n_trials  = 1000

rates = np.random.normal(mean_rate, std_dev, n_trials)
print(f'Mean: {rates.mean():.1f}')
print(f'Std:  {rates.std():.1f}')

The mean np.mean(data) is the average. The standard deviation np.std(data) measures spread — how much data varies around the mean.

🦌 Ilya says: Measurement noise in NMA experiments is nearly always modelled as Gaussian. Knowing this distribution = 30% of NMA stats done!