variance in normal distribution

Question

I recently started studying statistics. Please clarify following:

Suppose there are 2 normal distributions with same mean and different variance say $\sigma_1 > \sigma_2$. Then normal distribution curve for $\sigma_1$ has higher peak at mean and less spread than 2nd curve with lower variance $\sigma_2$. I feel it should be other way round right. High Variance means points are more far away from mean. So high variance curve should have more spread and less peaking at mean right? (compared to lesser variance normal distribution curve).

Please explain where i am thinkking wrongly.

Answer 1

I plot below three normal distributions with different variance and the same mean. Variances are, per color: blue > red > coral. So the result agrees with your intuition. The higher the variance the more spread the curve and lower peak.

Code used below:

import matplotlib.pyplot as plt
import scipy.stats
import numpy as np


x_min = 0.0
x_max = 16.0

mean = 8.0 
std = 2.0

x = np.linspace(x_min, x_max, 100)

y = scipy.stats.norm.pdf(x,mean,std)
y2 = scipy.stats.norm.pdf(x,mean,2*std)
y3 = scipy.stats.norm.pdf(x,mean,1.5*std)

plt.plot(x,y, color='coral')
plt.plot(x,y2, color='blue')
plt.plot(x,y3, color='red')

plt.grid()

plt.xlim(x_min,x_max)
plt.ylim(0,0.25)


plt.xlabel('x')
plt.ylabel('Normal Distribution')

plt.show()