Exercise 5.9

import numpy as np
import pandas as pd

from sklearn.datasets import load_boston

%matplotlib inline

boston = load_boston()
df = pd.DataFrame(boston.data, columns=boston.feature_names)
df['MEDV'] = pd.Series(boston.target)
medv = df['MEDV']
df.head()

	CRIM	ZN	INDUS	NOX	RM	AGE	DIS	RAD	TAX	PTRATIO	B	LSTAT	MEDV
0	0.00632	18.0	2.31	0.538	6.575	65.2	4.0900	1.0	296.0	15.3	396.90	4.98	24.0
1	0.02731	0.0	7.07	0.469	6.421	78.9	4.9671	2.0	242.0	17.8	396.90	9.14	21.6
2	0.02729	0.0	7.07	0.469	7.185	61.1	4.9671	2.0	242.0	17.8	392.83	4.03	34.7
3	0.03237	0.0	2.18	0.458	6.998	45.8	6.0622	3.0	222.0	18.7	394.63	2.94	33.4
4	0.06905	0.0	2.18	0.458	7.147	54.2	6.0622	3.0	222.0	18.7	396.90	5.33	36.2

(a)

mu = medv.mean()

(b)

medv.std()/np.sqrt(len(df))

0.40886114749753505

(c)

means = [medv.sample(n = len(df), replace=True).mean() for _ in range(1000)]
np.std(means)

0.4126021332293619

(d)

SE = np.std(means)
print(mu - 2*SE, mu + 2*SE)

21.7076020577 23.3580105906

(e)

medv.median()

21.2

(f)

medians = [medv.sample(n = len(df), replace=True).median() for _ in range(1000)]
np.std(medians)

0.37716367799670181

(g)

medv.quantile(.1)

12.75

(h)

quantiles = [medv.sample(n = len(df), replace=True).quantile(.1) for _ in range(1000)]
np.std(quantiles)x

0.50477123531358237