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. Presentation of Descriptive Statistics 2. Presentation of Evidence 3. Some people understand subject matter better with visual aids 4. Provide a sense of the underlying data generating process (scatterplots)
f(x) 0.00 0.02 0.04 0.06 0.08 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. Normal Density Plot 3σ 2σ σ σ 2σ 3σ -20-10 0 10 20 x
Mean, Median, Mode What is the Distribution? Gives us a picture of the variability and central tendency.. The Normal Distribution Mean = median = mode Skew is zero 68% of values fall between 1 SD 95% of values fall between 2 SDs 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 S 2 = (n -1) 2 ( X X ) 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 Googles- 199 Pallitto 189 Homer 187 3.5 3 2.5 2 1.5 1 0.5 0 Weight Class Intervals of Donut-Munching Professors 130-150 151-185 186-210 211-240 241-270 271-310 311+ Number Schnickerso 165 Smuggle 165 Boehmer 151 Levin 148 Queeny 132 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 Number of Students 14 12 10 8 6 4 2 0 A A- B+ B B- C+ C C- D+ D D- F Grade
X X- mean x-mean squared Smuggle 165-29.6 875.2 Bopsey 213 18.4 339.2 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 2480.1 49.8 The Standard Deviation = 165.2 pounds.
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 σ 2 = 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: Pop 1: 50 + 15 Pop 2 = 50 + 24 Maka variasi pop 1 lebih kecil Cara lain: dibandingkan KK Pop 1 : 27 + 9, KK=9/27= 0.333 Pop 2 : 43 + 11 KK = 11/43 = 0.256 Populasi yang lebih beragam adalah yang memiliki KK lebih tinggi.