# Understanding the distribution of the continuous data using the histogram

This topic explains the method to identify the distribution of a continuous variable using the histogram.

## Data ingestion

Python library is a collection of functions and methods that allows you to perform many actions without writing your code. To make use of the functions in a module, you’ll need to import the module with an import statement.

``````import numpy as np
import scipy.stats
import pandas as pd
``````
``````import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
``````
``````data = pd.read_csv('petroleum.csv')
``````

``````data.info()
``````

result:

``````<class 'pandas.core.frame.DataFrame'>
RangeIndex: 216 entries, 0 to 215
Data columns (total 5 columns):
Year             216 non-null int64
Geography        216 non-null object
Import           216 non-null float64
Export           216 non-null float64
CO2 Emissions    216 non-null float64
dtypes: float64(3), int64(1), object(1)
memory usage: 8.5+ KB
``````
``````data.head(4)
``````

result:

Year Geography Import Export CO2 Emissions
0 1980 Africa 618.184 5428.078 525.605046
1 1981 Africa 609.270 3964.097 519.408287
2 1982 Africa 557.209 3458.547 558.221545
3 1983 Africa 477.787 3394.148 586.002081

## Histogram

A histogram is an accurate representation of the distribution of numerical data.

``````plt.figure(figsize=(20,5))
plt.subplot(1,2,1);
data.Import.plot(kind='hist',histtype='step',bins=50)
plt.axvline(data.Import.mean(),c='red',label = 'Mean')
plt.axvline(data.Import.median(),c='green',linestyle='--',label = 'Median')
plt.axvline(data.Import.quantile(0.25),c='blue',linestyle=':',label = '0.25 quantile')
plt.axvline(data.Import.quantile(0.75),c='blue',linestyle=':',label = '0.75 quantile')
plt.axis(xmin=-100,xmax=25000)
plt.title('Petroleum Import',fontweight="bold",fontsize = 20)
plt.xlabel('barrels per day',fontweight="bold",fontsize = 15)
plt.ylabel('Frequency',fontweight="bold",fontsize = 15)
plt.xticks(fontweight="bold",fontsize = 10)
plt.yticks(fontweight="bold",fontsize = 10)
plt.legend(loc=1, prop={'size': 15})

plt.subplot(1,2,2);
data.Export.plot(kind='hist',histtype='step',bins=50)
plt.axvline(data.Export.mean(),c='red',label = 'Mean')
plt.axvline(data.Export.median(),c='green',linestyle='--',label = 'Median')
plt.axvline(data.Export.quantile(0.25),c='blue',linestyle=':',label = '0.25 quantile')
plt.axvline(data.Export.quantile(0.75),c='blue',linestyle=':',label = '0.75 quantile')
plt.axis(xmin=-100,xmax=25000)
plt.title('Petroleum Export',fontweight="bold",fontsize = 20)
plt.xlabel('barrels per day',fontweight="bold",fontsize = 15)
plt.ylabel('Frequency',fontweight="bold",fontsize = 15)
plt.xticks(fontweight="bold",fontsize = 10)
plt.yticks(fontweight="bold",fontsize = 10)
plt.legend(loc=1, prop={'size': 15})

plt.show()
``````

The above distribution comparision shows that the most of the export data is around 2100 and 5300 barrels per day. The most of the petroleum import is around 750 and 11000 barrels per day. But as per the calculated median from the above two distributions, the import data is more positively skewed due to outliers compared to export data.

## Probability density function:

• Representing the distribution for a continous variable
• Probability of a particular outcome is always zero
• The probability density function is nonnegative everywhere
• The integral over the entire space or area under the curve is equal to one.

``````# Probability density curve

plt.figure(figsize=(10,5))
data.Export.plot(kind='hist',histtype='step',bins=30,density=True)
data.Export.plot.density(bw_method=.09)
plt.axis(xmin=-0,xmax=20000)
plt.title("Probability density curve",fontweight="bold",fontsize=20)
plt.xlabel('barrels per day',fontweight="bold",fontsize = 15)
plt.ylabel('Density',fontweight="bold",fontsize = 15)
plt.xticks(fontweight="bold",fontsize = 10)
plt.yticks(fontweight="bold",fontsize = 10)
plt.legend(loc=1, prop={'size': 15})
plt.show()
``````

The above distribution is positive skewed. A distribution is positively skewed if the scores fall toward the lower side of the scale and there are very few higher scores. Positively skewed data is also referred to as skewed to the right because that is the direction of the ‘long tail end’ of the chart.

### References :

1. https://www.eia.gov/
2. https://stackoverflow.com/