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

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

In [ ]:

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

Out[ ]:

In [ ]:

```
#standard deviation of list
np.std(x)
```

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

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```
#mean
b.mean()
```

Out[ ]:

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

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```
#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[ ]:

In [ ]:

```
ex3.mean()
```

Out[ ]:

In [ ]:

```
ex3.std()
```

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In [ ]:

```
#deviation
ex2.std()
```

Out[ ]:

In [ ]:

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

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