Teorema limit pusat

Pengantar Statistika di Python

Maggie Matsui

Content Developer, DataCamp

Melempar dadu 5 kali

die = pd.Series([1, 2, 3, 4, 5, 6])

# Lempar 5 kali
samp_5 = die.sample(5, replace=True)
print(samp_5)

array([3, 1, 4, 1, 1])

np.mean(samp_5)

2.0

dadu enam sisi

# Lempar 5 kali dan ambil rerata
samp_5 = die.sample(5, replace=True)
np.mean(samp_5)

4.4

samp_5 = die.sample(5, replace=True)
np.mean(samp_5)

3.8

Ulangi 10 kali:

sample_means = []

for i in range(10):

  samp_5 = die.sample(5, replace=True)
  sample_means.append(np.mean(samp_5))

print(sample_means)

[3.8, 4.0, 3.8, 3.6, 3.2, 4.8, 2.6,
3.0, 2.6, 2.0]

Distribusi penarikan dari rerata sampel

histogram 10 rerata sampel

sample_means = []
for i in range(100):
    sample_means.append(np.mean(die.sample(5, replace=True)))

histogram 100 rerata sampel

sample_means = []
for i in range(1000):
    sample_means.append(np.mean(die.sample(5, replace=True)))

histogram 1000 rerata sampel

Distribusi penarikan suatu statistik makin mendekati distribusi normal saat jumlah percobaan meningkat.

histogram 10, 100, dan 1000 rerata sampel; jumlah lebih besar makin berbentuk lonceng

* Sampel harus acak dan independen

sample_sds = []
for i in range(1000):
  sample_sds.append(np.std(die.sample(5, replace=True)))

Distribusi 1000 simpangan baku sampel dari 5 lemparan dadu

sales_team = pd.Series(["Amir", "Brian", "Claire", "Damian"])

sales_team.sample(10, replace=True)

array(['Claire', 'Damian', 'Brian', 'Damian', 'Damian', 'Amir', 'Amir', 'Amir', 
      'Amir', 'Damian'], dtype=object)

sales_team.sample(10, replace=True)

array(['Brian', 'Amir', 'Brian', 'Claire', 'Brian', 'Damian', 'Claire', 'Brian', 
      'Claire', 'Claire'], dtype=object)

Distribusi proporsi sampel juga tampak normal

# Perkirakan nilai harapan dadu
np.mean(sample_means)

3.48

# Perkirakan proporsi "Claire"
np.mean(sample_props)

0.26

Distribusi penarikan rerata sampel dengan garis putus-putus di tengah

Pengantar Statistika di Python