Diskripsi: Types of Statistics dan Penyajian Data
• “summary ”, diskripsi data dengan angka:
– Mean, Median, Range, Standard Deviation, Variance, Min, Max, etc.
• Descriptive statistics of a POPULATION – mean – N population size – sum
• Inferential statistics of SAMPLES from a population. – Assumptions are made that the sample reflects the population in an unbiased form. – X mean – n sample size – sum
Simbul dan notasi statistik Data pengukuran suatu variabel ditulis dengan simbul (x) Untuk membedakan data digunakan Indeks (subscript): (x1, x2, x3,... xn, dst) Jika lebih dari satu variabel maka digunakan huruf lain, y, y dst. Contoh: Data LD (cm): 144+139+152+132+138+158 : x Huruf Ʃ : sigma, merupakan simbul perjumlahan
5 Ʃxi= (x1+x2+x3+X4+x5) = 144+ ........ + 138)= -------i=1 5 Ʃx2i= (x12+x22+x32+X42+x52) = (144)2+ ........ + (138)2= -------i=1 5 Ʃx1y1= (x1y1+x2y2+x3y3+X4y4+x5y5) = -------i=1
some univariate statistical terms: mode: value that occurs most frequently in a distribution (usually the highest point of curve)
median: value midway in the frequency distribution …half the area of curve is to right and other to left
mean: arithmetic average …sum of all observations divided by # of observations
range: measure of dispersion about mean (maximum minus minimum)
The “mean” of some data is the average score or value, Contoh: Berat Lahir (kg) sapi Potong dll Inferential mean of a sample: X=(X)/n Mean of a population: =(X)/N
The Range :
• r=h–l – Where h is high and l is low • the value between the minimum and maximum values of a variable. The Standard Deviation • A standardized measure of distance from the mean. • Very useful and something you do read about when making predictions or other statements about the data.
Measures of Dispersion : the spread or range of variability. • Measures of dispersion tell us about variability in the data. • Basic question: how much do values differ for a variable from the min to max, and distance among scores in between. We use: – Range – Standard Deviation – Variance
Organizing and Graphing Data: 1. 2. 3. 4.
Presentation of Descriptive Statistics Presentation of Evidence Some people understand subject matter better with visual aids Provide a sense of the underlying data generating process (scatterplots)
Normal Distribution The 68-95-99.7 Rule In the normal distribution with mean µ and standard deviation σ: 68% of the observations fall within σ of the mean µ. 95% of the observations fall within 2σ of the mean µ. 99.7% of the observations fall within 3σ of the mean µ.
0.04 0.02
3σ 2σ σ
0.00
f(x)
0.06
0.08
Normal Density Plot
-20
-10
σ 0
2σ 3σ 10
x
20
What is the Distribution? • Gives us a picture of the variability and central tendency. .
• Mean = median = mode • Skew is zero • 68% of values fall between 1 SD • 95% of values fall between 2 SDs
Mean, Median, Mode
The Normal Distribution
1
2
Standard Deviation Curve A
Curve B
A
B
Standard Deviation
S
=
2 ( X X ) (n - 1) =square root =sum (sigma) X=score for each point in data _ X=mean of scores for the variable n=sample size (number of observations or cases
Variance
2
S
=
2 ( X X ) (n - 1)
• Note that this is the same equation except for no square root taken.
Ranking Berat Badan (most to least) Zingers
308
Honkey-Doo
251
Calzone
227
Bopsey
213
Weight Class Intervals of Donut-Munching Professors 3.5 3 2.5 2
Number
1.5
Googles-
199
Pallitto
189
Homer
187
Schnickerso
165
Smuggle
165
Boehmer
151
Levin
148
Queeny
132
1 0.5 0 130-150 151-185 186-210 211-240 241-270 271-310
311+
Proportions of Donut-Eating Professors by Weight Class
130-150 151-185 186-210 211-240 241-270 271-310 311+
Distribution of Nilai Mahasiswa Genetika 14 12 10 Number of Students
8 6 4 2 0 A
A- B+ B
B- C+ C Grade
C- D+ D
D-
F
X
X- mean
x-mean squared
Smuggle
165
-29.6
Bopsey
213
18.4
Pallitto
189
-5.6
31.2
Homer
187
-7.6
57.5
Schnickerson
165
-29.6
875.2
Levin
148
-46.6
2170.0
Honkey-Doorey
251
56.4
3182.8
Zingers
308
113.4
12863.3
Boehmer
151
-43.6
1899.5
Queeny
132
-62.6
3916.7
Googles-boop
199
4.4
19.5
Calzone
227
32.4
1050.8
Mean
194.6
875.2 339.2
2480.1
The Standard Deviation = 165.2 pounds.
49.8
Populasi dan Sampel Munculnya variasi berhubungan dengan adanya perbedaan antara individu anggota populasi Salah satu ciri penting adalah nilai
rataannya
Pengamatan data Kuantitatif : •keragaman kontinyu, • distribusi normal,
•pengelompokan disekitar nilai rataan
-
I SD
X
1 SD
+
Nilai/Ukuran Statistik: Rataan ( X atau μ ) dari data X1, X2 …. Xn = Σ (X)/n = (X1 + X2 ….+Xn) n n= jumlah pengamatan X1,2,3,… n = data populasi/Sample Ragam Populasi (simpangan/beda dng nilai rataan) mrpk derajat keragaman populasi σ2 = Σ (X-X)2 (n-1)
Simpangan Baku: Ukuran keragaman populasi yang tepat (akar dari ragam) SD = (X1- X) + (X2 – X)……… (Xn – X)
(n-1)
Koefisien keragaman (Variasi)* : simpangan baku dalam nilai persen dari nilai rataan
KK =
SD
X 100 %
X
Jika ingin membandingkan dua populasi mana yang lebih beragam (Jika rataan populasi hampir sama, maka koefisien keragaman dari pop yang lebih tinggi dianggap lebih beragam)
Misalnya Pop = X + SD ., Jika:
Cara lain: dibandingkan KK
Pop 1: 50 + 15
Pop 1 : 27 + 9 , KK=9/27= 0.333
Pop 2 = 50 + 24
Pop 2 : 43 + 11
Maka variasi pop 1 lebih kecil
Populasi yang lebih beragam adalah yang memiliki KK lebih tinggi.
KK = 11/43 = 0.256
