Probability and Statistics

Mean and Std with Python

\text{mean} = \mu = \frac{1}{n}\sum_{i = 1}^n x_i

\text{standard deviation} = \sigma = \sqrt{\frac{1}{n}\sum_{i = 1}^n (x_i - \mu)^2}

In [ ]:

#mean of a list
x = [3, 5, 7, 9, 11]
np.mean(x)

Out[ ]:

7.0

In [ ]:

#standard deviation of list
np.std(x)

Out[ ]:

2.8284271247461903

In [ ]:

#Binomial distribution with n = 20, p = 0.5
b = stats.binom(20, 0.5)

In [ ]:

#mean
b.mean()

Out[ ]:

10.0

In [ ]:

#plot
plt.bar(range(21), b.pmf(range(21)))

Out[ ]:

<BarContainer object of 21 artists>

In [ ]:

#another example
#Binomial n = 50, p = 0.3
ex2 = stats.binom(50, 0.3)
ex3 = stats.binom(20, 0.3)

In [ ]:

#mean
ex2.mean()

Out[ ]:

15.0

In [ ]:

ex3.mean()

Out[ ]:

6.0

In [ ]:

ex3.std()

Out[ ]:

2.0493901531919194

In [ ]:

#deviation
ex2.std()

Out[ ]:

3.24037034920393

In [ ]:

#plot
plt.bar(range(51), ex2.pmf(range(51)))
plt.bar(range(21), ex3.pmf(range(21)))

Out[ ]:

<BarContainer object of 21 artists>