作業一：判斷資料趨勢（正偏/負偏/對稱）

1. 安裝套件

# Pandas and numpy for data manipulation import pandas as pd import numpy as np

# matplotlib for plotting import matplotlib.pyplot as plt import matplotlib from scipy import stats from scipy.stats import norm # Set text size matplotlib.rcParams['font.size'] = 18 # Seaborn import seaborn as sns sns.set_context('talk', font_scale=1.2);

2. 顯示資料集

df = pd.read_csv('hw1常態分配資料集.csv') df.columns = ['Object','A1','A2','A3'] df

3. 判斷各欄位的分佈趨勢

data = df.A1 sns.distplot(data, fit=norm, rug=True, hist=False) # sns.displot(data,kind="kde",rug=True) (mu, sigma) = norm.fit(data) print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma)) plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],loc='best') #圖中的藍色線標題 plt.ylabel('Frequency') plt.title('Distribution') plt.show()

/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).
  warnings.warn(msg, FutureWarning)
/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2103: FutureWarning: The `axis` variable is no longer used and will be removed. Instead, assign variables directly to `x` or `y`.
  warnings.warn(msg, FutureWarning)

 mu = 47.40 and sigma = 34.71

data = df.A2 sns.distplot(data, fit=norm, rug=True, hist=False) # sns.displot(data,kind="kde",rug=True) (mu, sigma) = norm.fit(data) print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma)) plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],loc='best') plt.ylabel('Frequency') plt.title('Distribution') plt.show()

/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).
  warnings.warn(msg, FutureWarning)
/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2103: FutureWarning: The `axis` variable is no longer used and will be removed. Instead, assign variables directly to `x` or `y`.
  warnings.warn(msg, FutureWarning)

 mu = 56.60 and sigma = 29.86

data = df.A3 sns.distplot(data, fit=norm, rug=True, hist=False) # sns.displot(data,kind="kde",rug=True) (mu, sigma) = norm.fit(data) print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma)) plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],loc='best') plt.ylabel('Frequency') plt.title('Distribution') plt.show()

/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).
  warnings.warn(msg, FutureWarning)
/shared-libs/python3.7/py/lib/python3.7/site-packages/seaborn/distributions.py:2103: FutureWarning: The `axis` variable is no longer used and will be removed. Instead, assign variables directly to `x` or `y`.
  warnings.warn(msg, FutureWarning)

 mu = 34.10 and sigma = 25.61

4. 各欄位是否符合常態分佈？

Yes, 因為pvalue > 0.05

a1 = stats.kstest(df.A1,'norm',(mu,sigma)) a2 = stats.kstest(df.A2,'norm',(mu,sigma)) a3 = stats.kstest(df.A3,'norm',(mu,sigma)) print(a1) print(a2) print(a3)

KstestResult(statistic=0.19503570922074231, pvalue=0.77411419842939)
KstestResult(statistic=0.20312353546352058, pvalue=0.7325635545497902)
KstestResult(statistic=0.31190213473186645, pvalue=0.23144054607793352)

5. 結論

A1, A2, A3從圖中可以觀察到都是正偏斜資料，三個欄位各自的平均數皆大於中位數。