# Lesson 7¶

### Outliers¶

In [1]:
import pandas as pd
import sys

In [2]:
print 'Python version ' + sys.version
print 'Pandas version: ' + pd.__version__

Python version 2.7.5 |Anaconda 2.1.0 (64-bit)| (default, Jul  1 2013, 12:37:52) [MSC v.1500 64 bit (AMD64)]
Pandas version: 0.15.2

In [3]:
# Create a dataframe with dates as your index
States = ['NY', 'NY', 'NY', 'NY', 'FL', 'FL', 'GA', 'GA', 'FL', 'FL']
data = [1.0, 2, 3, 4, 5, 6, 7, 8, 9, 10]
idx = pd.date_range('1/1/2012', periods=10, freq='MS')
df1 = pd.DataFrame(data, index=idx, columns=['Revenue'])
df1['State'] = States

# Create a second dataframe
data2 = [10.0, 10.0, 9, 9, 8, 8, 7, 7, 6, 6]
idx2 = pd.date_range('1/1/2013', periods=10, freq='MS')
df2 = pd.DataFrame(data2, index=idx2, columns=['Revenue'])
df2['State'] = States

In [4]:
# Combine dataframes
df = pd.concat([df1,df2])
df

Out[4]:
Revenue State
2012-01-01 1 NY
2012-02-01 2 NY
2012-03-01 3 NY
2012-04-01 4 NY
2012-05-01 5 FL
2012-06-01 6 FL
2012-07-01 7 GA
2012-08-01 8 GA
2012-09-01 9 FL
2012-10-01 10 FL
2013-01-01 10 NY
2013-02-01 10 NY
2013-03-01 9 NY
2013-04-01 9 NY
2013-05-01 8 FL
2013-06-01 8 FL
2013-07-01 7 GA
2013-08-01 7 GA
2013-09-01 6 FL
2013-10-01 6 FL

# Ways to Calculate Outliers¶

Note: Average and Standard Deviation are only valid for gaussian distributions.

In [5]:
# Method 1

# make a copy of original df
newdf = df.copy()

newdf['x-Mean'] = abs(newdf['Revenue'] - newdf['Revenue'].mean())
newdf['1.96*std'] = 1.96*newdf['Revenue'].std()
newdf['Outlier'] = abs(newdf['Revenue'] - newdf['Revenue'].mean()) > 1.96*newdf['Revenue'].std()
newdf

Out[5]:
Revenue State x-Mean 1.96*std Outlier
2012-01-01 1 NY 5.75 5.200273 True
2012-02-01 2 NY 4.75 5.200273 False
2012-03-01 3 NY 3.75 5.200273 False
2012-04-01 4 NY 2.75 5.200273 False
2012-05-01 5 FL 1.75 5.200273 False
2012-06-01 6 FL 0.75 5.200273 False
2012-07-01 7 GA 0.25 5.200273 False
2012-08-01 8 GA 1.25 5.200273 False
2012-09-01 9 FL 2.25 5.200273 False
2012-10-01 10 FL 3.25 5.200273 False
2013-01-01 10 NY 3.25 5.200273 False
2013-02-01 10 NY 3.25 5.200273 False
2013-03-01 9 NY 2.25 5.200273 False
2013-04-01 9 NY 2.25 5.200273 False
2013-05-01 8 FL 1.25 5.200273 False
2013-06-01 8 FL 1.25 5.200273 False
2013-07-01 7 GA 0.25 5.200273 False
2013-08-01 7 GA 0.25 5.200273 False
2013-09-01 6 FL 0.75 5.200273 False
2013-10-01 6 FL 0.75 5.200273 False
In [6]:
# Method 2
# Group by item

# make a copy of original df
newdf = df.copy()

State = newdf.groupby('State')

newdf['Outlier'] = State.transform( lambda x: abs(x-x.mean()) > 1.96*x.std() )
newdf['x-Mean'] = State.transform( lambda x: abs(x-x.mean()) )
newdf['1.96*std'] = State.transform( lambda x: 1.96*x.std() )
newdf

Out[6]:
Revenue State Outlier x-Mean 1.96*std
2012-01-01 1 NY False 5.00 7.554813
2012-02-01 2 NY False 4.00 7.554813
2012-03-01 3 NY False 3.00 7.554813
2012-04-01 4 NY False 2.00 7.554813
2012-05-01 5 FL False 2.25 3.434996
2012-06-01 6 FL False 1.25 3.434996
2012-07-01 7 GA False 0.25 0.980000
2012-08-01 8 GA False 0.75 0.980000
2012-09-01 9 FL False 1.75 3.434996
2012-10-01 10 FL False 2.75 3.434996
2013-01-01 10 NY False 4.00 7.554813
2013-02-01 10 NY False 4.00 7.554813
2013-03-01 9 NY False 3.00 7.554813
2013-04-01 9 NY False 3.00 7.554813
2013-05-01 8 FL False 0.75 3.434996
2013-06-01 8 FL False 0.75 3.434996
2013-07-01 7 GA False 0.25 0.980000
2013-08-01 7 GA False 0.25 0.980000
2013-09-01 6 FL False 1.25 3.434996
2013-10-01 6 FL False 1.25 3.434996
In [7]:
# Method 2
# Group by multiple items

# make a copy of original df
newdf = df.copy()

StateMonth = newdf.groupby(['State', lambda x: x.month])

newdf['Outlier'] = StateMonth.transform( lambda x: abs(x-x.mean()) > 1.96*x.std() )
newdf['x-Mean'] = StateMonth.transform( lambda x: abs(x-x.mean()) )
newdf['1.96*std'] = StateMonth.transform( lambda x: 1.96*x.std() )
newdf

Out[7]:
Revenue State Outlier x-Mean 1.96*std
2012-01-01 1 NY False 4.5 12.473364
2012-02-01 2 NY False 4.0 11.087434
2012-03-01 3 NY False 3.0 8.315576
2012-04-01 4 NY False 2.5 6.929646
2012-05-01 5 FL False 1.5 4.157788
2012-06-01 6 FL False 1.0 2.771859
2012-07-01 7 GA False 0.0 0.000000
2012-08-01 8 GA False 0.5 1.385929
2012-09-01 9 FL False 1.5 4.157788
2012-10-01 10 FL False 2.0 5.543717
2013-01-01 10 NY False 4.5 12.473364
2013-02-01 10 NY False 4.0 11.087434
2013-03-01 9 NY False 3.0 8.315576
2013-04-01 9 NY False 2.5 6.929646
2013-05-01 8 FL False 1.5 4.157788
2013-06-01 8 FL False 1.0 2.771859
2013-07-01 7 GA False 0.0 0.000000
2013-08-01 7 GA False 0.5 1.385929
2013-09-01 6 FL False 1.5 4.157788
2013-10-01 6 FL False 2.0 5.543717
In [8]:
# Method 3
# Group by item

# make a copy of original df
newdf = df.copy()

State = newdf.groupby('State')

def s(group):
group['x-Mean'] = abs(group['Revenue'] - group['Revenue'].mean())
group['1.96*std'] = 1.96*group['Revenue'].std()
group['Outlier'] = abs(group['Revenue'] - group['Revenue'].mean()) > 1.96*group['Revenue'].std()
return group

Newdf2 = State.apply(s)
Newdf2

Out[8]:
Revenue State x-Mean 1.96*std Outlier
2012-01-01 1 NY 5.00 7.554813 False
2012-02-01 2 NY 4.00 7.554813 False
2012-03-01 3 NY 3.00 7.554813 False
2012-04-01 4 NY 2.00 7.554813 False
2012-05-01 5 FL 2.25 3.434996 False
2012-06-01 6 FL 1.25 3.434996 False
2012-07-01 7 GA 0.25 0.980000 False
2012-08-01 8 GA 0.75 0.980000 False
2012-09-01 9 FL 1.75 3.434996 False
2012-10-01 10 FL 2.75 3.434996 False
2013-01-01 10 NY 4.00 7.554813 False
2013-02-01 10 NY 4.00 7.554813 False
2013-03-01 9 NY 3.00 7.554813 False
2013-04-01 9 NY 3.00 7.554813 False
2013-05-01 8 FL 0.75 3.434996 False
2013-06-01 8 FL 0.75 3.434996 False
2013-07-01 7 GA 0.25 0.980000 False
2013-08-01 7 GA 0.25 0.980000 False
2013-09-01 6 FL 1.25 3.434996 False
2013-10-01 6 FL 1.25 3.434996 False
In [9]:
# Method 3
# Group by multiple items

# make a copy of original df
newdf = df.copy()

StateMonth = newdf.groupby(['State', lambda x: x.month])

def s(group):
group['x-Mean'] = abs(group['Revenue'] - group['Revenue'].mean())
group['1.96*std'] = 1.96*group['Revenue'].std()
group['Outlier'] = abs(group['Revenue'] - group['Revenue'].mean()) > 1.96*group['Revenue'].std()
return group

Newdf2 = StateMonth.apply(s)
Newdf2

Out[9]:
Revenue State x-Mean 1.96*std Outlier
2012-01-01 1 NY 4.5 12.473364 False
2012-02-01 2 NY 4.0 11.087434 False
2012-03-01 3 NY 3.0 8.315576 False
2012-04-01 4 NY 2.5 6.929646 False
2012-05-01 5 FL 1.5 4.157788 False
2012-06-01 6 FL 1.0 2.771859 False
2012-07-01 7 GA 0.0 0.000000 False
2012-08-01 8 GA 0.5 1.385929 False
2012-09-01 9 FL 1.5 4.157788 False
2012-10-01 10 FL 2.0 5.543717 False
2013-01-01 10 NY 4.5 12.473364 False
2013-02-01 10 NY 4.0 11.087434 False
2013-03-01 9 NY 3.0 8.315576 False
2013-04-01 9 NY 2.5 6.929646 False
2013-05-01 8 FL 1.5 4.157788 False
2013-06-01 8 FL 1.0 2.771859 False
2013-07-01 7 GA 0.0 0.000000 False
2013-08-01 7 GA 0.5 1.385929 False
2013-09-01 6 FL 1.5 4.157788 False
2013-10-01 6 FL 2.0 5.543717 False

Assumign a non gaussian distribution (if you plot it, it will not look like a normal distribution)

In [10]:
# make a copy of original df
newdf = df.copy()

State = newdf.groupby('State')

newdf['Lower'] = State['Revenue'].transform( lambda x: x.quantile(q=.25) - (1.5*(x.quantile(q=.75)-x.quantile(q=.25))) )
newdf['Upper'] = State['Revenue'].transform( lambda x: x.quantile(q=.75) + (1.5*(x.quantile(q=.75)-x.quantile(q=.25))) )
newdf['Outlier'] = (newdf['Revenue'] < newdf['Lower']) | (newdf['Revenue'] > newdf['Upper'])
newdf

Out[10]:
Revenue State Lower Upper Outlier
2012-01-01 1 NY -7.000 19.000 False
2012-02-01 2 NY -7.000 19.000 False
2012-03-01 3 NY -7.000 19.000 False
2012-04-01 4 NY -7.000 19.000 False
2012-05-01 5 FL 2.625 11.625 False
2012-06-01 6 FL 2.625 11.625 False
2012-07-01 7 GA 6.625 7.625 False
2012-08-01 8 GA 6.625 7.625 True
2012-09-01 9 FL 2.625 11.625 False
2012-10-01 10 FL 2.625 11.625 False
2013-01-01 10 NY -7.000 19.000 False
2013-02-01 10 NY -7.000 19.000 False
2013-03-01 9 NY -7.000 19.000 False
2013-04-01 9 NY -7.000 19.000 False
2013-05-01 8 FL 2.625 11.625 False
2013-06-01 8 FL 2.625 11.625 False
2013-07-01 7 GA 6.625 7.625 False
2013-08-01 7 GA 6.625 7.625 False
2013-09-01 6 FL 2.625 11.625 False
2013-10-01 6 FL 2.625 11.625 False

Author: David Rojas