03 Z-score introduction

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

khanacademy

\[ Z = \frac{x - \mu}{\sigma} \]

x = np.array([2, 2, 3, 2, 5, 1, 6])

mu = np.mean(x)
sigma = np.std(x)

z_score = (x - mu) / sigma

# alternative way
z_score_ = stats.zscore(x)

z_score

array([-0.59160798, -0.59160798,  0.        , -0.59160798,  1.18321596,
       -1.18321596,  1.77482393])

z_score_

array([-0.59160798, -0.59160798,  0.        , -0.59160798,  1.18321596,
       -1.18321596,  1.77482393])

df = DataFrame({'lengths of wigned trutles (cm)': x, 'Z-score':z_score_})

df

	lengths of wigned trutles (cm)	Z-score
0	2	-0.591608
1	2	-0.591608
2	3	0.000000
3	2	-0.591608
4	5	1.183216
5	1	-1.183216
6	6	1.774824