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Basic Statistics in Python

Learn how to perform basic statistical operations using Python.

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Import Data

Let us import a dataset to perform our statistics. We will be looking at the consumption of alcohol by country in 2010.

In [2]:
data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/2010_alcohol_consumption_by_country.csv')
df = data[0:10]

table = FF.create_table(df)
py.iplot(table, filename='alcohol-data-sample')
Out[2]:

Mean and Variance

Two of the most basic statistical operations are the mean $\mu$ and standard deviation $\sigma$ of a one-dimension array of data, that is, a sequence of numeric values. The mean of a set of numbers $x_1, ..., x_N$ is defined as:

$$\begin{align*} \mu = \sum_{i=1}^N{x_i} \end{align*} $$

The mean is used colloquially as the average of a set of values. The standard deviation on the other hand is a statistical metric that describes the spread of the data, or how far the values are from the mean. The standard deviation of a set of data is defined as:

$$\begin{align*} \sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^{N}{(x_i-\mu)^2}} \end{align*} $$
In [3]:
mean = np.mean(data['alcohol'])
st_dev = np.std(data['alcohol'])

print("The mean is %r") %(mean)
print("The standard deviation is %r") %(st_dev)
The mean is 6.2083769633507835
The standard deviation is 4.130671000635401

Secondary Statistics

We can also compute other statistics such as the median, maximum and minimum of the data

In [4]:
median = np.median(data['alcohol'])
maximum = np.max(data['alcohol'])
minimum = np.min(data['alcohol'])

print("The median is %r") %(median)
print("The maximum is %r") %(maximum)
print("The minimum is %r") %(minimum)
The median is 6.4000000000000004
The maximum is 17.5
The minimum is 0.10000000000000001

Visualize the Statistics

We can visualize these statistics by producing a Plotly box or Violin chart.

In [5]:
y = data['alcohol'].values.tolist()

fig = FF.create_violin(y, title='Violin Plot', colors='#604d9e')
py.iplot(fig, filename='alcohol-violin-visual')
Out[5]:
In [6]:
y = data['alcohol'].values.tolist()

trace = go.Box(
    y=y,
    name = 'Box Plot',
    boxpoints='all',
    jitter=0.3,
    marker = dict(
        color = 'rgb(214,12,140)',
    ),
)

layout = go.Layout(
    width=500,
    yaxis=dict(
        title='Alcohol Consumption by Country',
        zeroline=False
    ),
)

data = [trace]
fig= go.Figure(data=data, layout=layout)
py.iplot(fig, filename='alcohol-box-plot')
Out[6]:
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