Central tendency mean median modus
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Achmad Zain NuruddinIAIN Sunan Ampel Surabaya
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Notasi / simbol penjumlahan
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Jika ada jumlah bilangan berikut ini 8, 3, 5, 12, 10, maka mean nya adalah:
X = X1+X2+X3+X4+X5/N X = 8+3+5+12+10/5 =7,6
Jika ada bilangan 5, 8, 6, 2,masing masing terjadi dengan frekwensi 3,2,4,1, maka mean nya adalah:
X = (3)5+2(8)+4(6)+(1)2/3+2+4+1 =5,7
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Jika ada bilangan nilai kuis 70 dan 90 dan UAS 85 diberi bobot 3 kali dari nilai kuis maka mean nya adalah:
X = (1)70+(1)90+(3)85/1+1+3 = 415/5 = 83∑wX∑w
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Mean geometrik dari bulangan 2, 4, 8 adalah:
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Median adalah nilai tengah dari sejumlah bilangan yang ada dan modus adalah nilai atau angka yang paling banyak frekwensi kemunculannya.
Contoh; bilangan berikut ini 5,6,8,4,3,8,4,8,8,10 memiliki median 6 dan memiliki modus 8.
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Mean, Median dan Modus
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meanmedianmodus modusmedianmean
Kemiringan positiveKemiringan negative
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Jika suatu kumpulan data yg disusun berdasarkan ukuran kecil besarnya, dan nilai tengah yg membagi kumpulan data tersebut menjadi dua bgaian yg sama, maka mean tersebut sama dengan median dari data bersangkutan.
Nilai nilai yg dinyatakan Q1, Q2 dan Q3 masing2 disebut kuartil pertama, kedua dan ketiga, dan Q2 sama dengan mediannya.
Nilai2 yg membagi data 10 disebut decil, dinyatakan dengan simbol D1, D2, D3…….D9, di mana D5 sama dengan mediannya.
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Begitu juga nilai2 yg membagi data 100 disebut persentil, disimbolkan dengan P1, P2, P3…. P99, dimana P50 merupakan mediannya.
Dan P25 serta P75 masing2 berkoresponden dengan kuartil pertama dan ketiga
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Carilah mean dari tinggi badan mahasiswa di PT xyz.
Class Class (TB)(TB)
MidpointMidpoint(x)(x)
FrekwensiFrekwensi (f)(f)
fxfx
60 – 6260 – 62
63 – 6563 – 65
66 – 6866 – 68
69 – 7169 – 71
72 -7472 -74
6161
6464
6767
7070
7373
55
1818
4242
2727
88
305305
11521152
28142814
18901890
584584N=∑f N=∑f =100=100
∑∑fx =6745fx =674510
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1. Population Mean2. Sample Mean
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Sample Median
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Median class nya adalah: 50-23=27 (69-66)/42=0.071429 (0.071429x26)+65.5 =67.35714 67.35714+0.071429 =67.42857 (67.35714+ 67.42857)/2 =67.39286
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Menghitung Median dari grouped data
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m = sample median. n = total number of items in the
distribution. F = sum of all the class frequencies up to,
but not including, the median class. fm= frequency of the median class w = class interval width Lm = lower limit of the median class
interval
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Menghitung Mode dari grouped data.
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Mo = mode. LMo = lower limit of the modal class. D1 = frequency of the modal class minus
the frequency of the class directly below it.
D2 = frequency of the modal class minus the frequency of the class directly above it.
w = width of the modal class interval
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Mode = 66.11 Median = 67.39 Mean = 67.45
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