[PSDS] 예제:인구에 따른 살인 비율의 위치 추정

평균, 절사 평균, 중간값¶

1단계 : 데이터 로드하기¶

In [ ]:

from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive

2단계: 데이터 확인하기¶

In [ ]:

STATE_CSV = '/content/drive/MyDrive/통계공부/PSDS/data/state.csv'

In [ ]:

import pandas as pd

state = pd.read_csv(STATE_CSV)
print(state.head(8))

         State  Population  Murder.Rate Abbreviation
0      Alabama     4779736          5.7           AL
1       Alaska      710231          5.6           AK
2      Arizona     6392017          4.7           AZ
3     Arkansas     2915918          5.6           AR
4   California    37253956          4.4           CA
5     Colorado     5029196          2.8           CO
6  Connecticut     3574097          2.4           CT
7     Delaware      897934          5.8           DE

3단계: 계산하기¶

In [ ]:

#평균
state['Population'].mean()

Out[ ]:

6162876.3

In [ ]:

#절사 평균
from scipy.stats import trim_mean

trim_mean(state['Population'], 0.1)

Out[ ]:

4783697.125

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#중앙값
state['Population'].median()

Out[ ]:

4436369.5

In [ ]:

#가중 평균
import numpy as np
np.average(state['Population'], weights=state['Population'])

Out[ ]:

13620491.638786951

In [ ]:

#가중 중간값

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pip install wquantiles

Collecting wquantiles
  Downloading wquantiles-0.6-py3-none-any.whl (3.3 kB)
Requirement already satisfied: numpy>=1.18 in /usr/local/lib/python3.10/dist-packages (from wquantiles) (1.23.5)
Installing collected packages: wquantiles
Successfully installed wquantiles-0.6

In [ ]:

import wquantiles

wquantiles.median(state['Murder.Rate'], weights=state['Population'])

Out[ ]:

4.4

• 가장 기본적인 위치 추정값은 평균 but. 극단값(outlier)에 민감할 수 있음

• 중간값, 절사평균과 같은 다른 방법들이 outlier나 이상데이터에 robust