08 Interquartile range (IQR)

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<iframe width="700" height="400" src="https://www.youtube.com/embed/qLYYHWYr8xI/" frameborder="0" allowfullscreen></iframe>

import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
from scipy import stats

khanacademy pandas.DataFrame.quantile

x_data = {'x': [4,4,6,7,10,11,12,14,15]}

y_data = {'y': [7, 9, 9, 10, 10, 11, 12, 12, 14]}

x_df = DataFrame(x_data)
y_df = DataFrame(y_data)

x_df.describe()

	x
count	9.000000
mean	9.222222
std	4.146618
min	4.000000
25%	6.000000
50%	10.000000
75%	12.000000
max	15.000000

y_df.describe()

	y
count	9.000000
mean	10.444444
std	2.068279
min	7.000000
25%	9.000000
50%	10.000000
75%	12.000000
max	14.000000

print(x_df.quantile(q=0.75))
print(x_df.quantile(q=0.75, interpolation='nearest'))

print(y_df.quantile(q=0.75))
print(y_df.quantile(q=0.75, interpolation='nearest'))

x    12.0
Name: 0.75, dtype: float64
x    12
Name: 0.75, dtype: int64
y    12.0
Name: 0.75, dtype: float64
y    12
Name: 0.75, dtype: int64

print(stats.iqr(x_df))
print(stats.iqr(y_df))

6.0
3.0

x_df['Rank'] = x_df.index + 1
x_df['Empirical_CDF'] = x_df['Rank'] / x_df.shape[0]
x_q_25 = x_df.x[x_df['Empirical_CDF']>=0.25].reset_index(drop=True)[0]
x_q_50 = x_df.x[x_df['Empirical_CDF']>=0.50].reset_index(drop=True)[0]
x_q_75 = x_df.x[x_df['Empirical_CDF']>=0.75].reset_index(drop=True)[0]

y_df['Rank'] = y_df.index + 1
y_df['Empirical_CDF'] = y_df['Rank'] / y_df.shape[0]
y_q_25 = y_df.y[y_df['Empirical_CDF']>=0.25].reset_index(drop=True)[0]
y_q_50 = y_df.y[y_df['Empirical_CDF']>=0.50].reset_index(drop=True)[0]
y_q_75 = y_df.y[y_df['Empirical_CDF']>=0.75].reset_index(drop=True)[0]

print(f'q 25 {x_q_25} q 50 {x_q_50} q 75 {x_q_75} => iqr = {x_q_75 - x_q_25}')
print(f'q 25 {y_q_25} q 50 {y_q_50} q 75 {y_q_75} => iqr = {y_q_75 - y_q_25}')

q 25 6 q 50 10 q 75 12 => iqr = 6
q 25 9 q 50 10 q 75 12 => iqr = 3