Latihan Ukuran Statistik

Tentukan mean, modus da median dari tabel distribusi frekuensi dibawah ini?
kelas f
12 – 16 12
17 – 21 3
22 – 26 15
27 – 31 10
32 – 36 4
37 – 41 8
42 – 46 7

Jawab:
i = 5 dan k = 7
TDF

a. Mean
xi = [12 + 16] : 2 = 28 : 2 = 14
M = [12 + 46] : 2 = 58 : 2 = 29
Cara langsung:
X- = ∑ fi.Xi : ∑ fi
= 1631 : 59
= 27,644

Cara pendugaan:
X- = M + [(∑ fi . di) : n]
= 29 + [(-80) : 59]
= 29 + (-1,356)
= 27,644

Jadi mean = 27,644


b. Modus
Kelas modus = 22 – 26
TBB = 21,5
d1 = 15 - 3 = 12
d2 = 15 - 10 = 5
Mo = TBB + i [d1 : (d1 + d2)]
= 21,5 + 5 [12 : (12 + 5)]
= 21,5 + 5 [12 : 17]
= 21,5 + 5 . 0,706
= 21,5 + 3,529
= 25,029
Jadi modus = 25,029


c. Median
Letak median = 59 : 2 = 29,5
Kelas median = 22 – 26 [memiliki frekuensi komulatif 30]
TBB = 21,5
TBA = 26,5
fme = 15
s = 29,5 – 15 = 14,5
s’ = 29,5 – 30 = 0,5
Cara 1:
Me = TBB + i (s : fme)
= 21,5 + 5 (14,5 : 15)
= 21,5 + 5 . 0,967
= 21,5 + 4,835
= 26,335

Cara 2:
Me = TBA – i (s’ : fme)
= 26,5 – 5 (0,5 : 15)
= 26,5 – 5 . 0,033
= 26,5 – 0,165
= 26,335

Jadi median = 26,335



Mata Kuliah Statistik I
Selasa, 02 Februari 2010