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# Mean and Std with Python

### Mean and Standard Deviation¶

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