Diskripsi: Types of Statistics dan Penyajian Data

Transkripsi

1 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

2 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): : x Huruf Ʃ : sigma, merupakan simbul perjumlahan 5 Ʃxi= (x1+x2+x3+x4+x5) = )= i=1 5 Ʃx2i= (x12+x22+x32+x42+x52) = (144) (138)2= i=1 5 Ʃx1y1= (x1y1+x2y2+x3y3+x4y4+x5y5) = i=1

3 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)

4 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.

5 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

6 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)

7 f(x) Normal Distribution The 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 x

8 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

9 Standard Deviation Curve A Curve B A B

10 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

11 Variance S 2 = (n -1) 2 ( X X ) Note that this is the same equation except for no square root taken.

12 Ranking Berat Badan (most to least) Zingers 308 Honkey-Doo 251 Calzone 227 Bopsey 213 Googles- 199 Pallitto 189 Homer Weight Class Intervals of Donut-Munching Professors Number Schnickerso 165 Smuggle 165 Boehmer 151 Levin 148 Queeny 132 Proportions of Donut-Eating Professors by Weight Class

13 Distribution of Nilai Mahasiswa Genetika Number of Students A A- B+ B B- C+ C C- D+ D D- F Grade

14 X X- mean x-mean squared Smuggle Bopsey Pallitto Homer Schnickerson Levin Honkey-Doorey Zingers Boehmer Queeny Googles-boop Calzone Mean The Standard Deviation = pounds.

15 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 +

16 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)

17 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: Pop 2 = Maka variasi pop 1 lebih kecil Cara lain: dibandingkan KK Pop 1 : , KK=9/27= Pop 2 : KK = 11/43 = Populasi yang lebih beragam adalah yang memiliki KK lebih tinggi.