STATISTIKA Oleh JOHAR WIRYAWAN Kuliah Statistika Program Studi Sistem Informasi Fakultas Sains dan Teknologi Universitas Islam Negeri “Syarif Hidayatullah” Jakarta

Pertemuan 01 PENDAHULUAN: Data dan Statistika . Pertemuan 01 PENDAHULUAN: Data dan Statistika

Materi Statistika sebagai Sains Macam Aplikasi Statistika Unsur-unsur Dasar Statistika Macam Data Pengumpulan Data Peranan Statistika Penyajian Data Diagram Distribusi/Sebaran Frekuensi

Definisi Statistika Statistika (merupakan cabang matematika) yang mempelajari teknik-teknik pengambilan keputusan terhadap suatu masalah dengan menggunakan sebagian keterangan kuantitatif dari masalah tersebut.

Berdasarkan definisi tsb maka kajian statistika meliputi : Tatacara pengumpulan data melalui percobaan, survey atau observasi Tatacara analisa data sehingga miudah diinterpretasi dan disimpulkan Tatacara menyimpulkan dan menginterpretasi

Population and Sample Inference on the population from the sample Use statistics to summarize features Use parameters to summarize features Inference on the population from the sample

Beberapa Istilah penting Model matematik dalam statistik merupakan gambaran bagi suatu masalah yang dinyatakan sebagai hubungan matematik Populasi adalah keseluruhan obyek pengamatan Contoh (sampel) bagian dari populasi yang digunakan untuk menerangkan ciri-ciri populasi induknya Parameter adalah data sebenarnya (ciri populasi) Fungsi statistik sebagai alat bantu untuk memecahkan masalah

Basic Concept Population: the set of all measurements of interest to the investigator Sample: a subset of measurements selected from the population of interest

Metoda Statistik Statistik Deskriptif Statistik Induktif / Inferensia Pengumpulan , pengolahan , penyajian dan analisa Statistik Induktif / Inferensia Pengambilan kesimpulan

Descriptive Statistics Collect Data E.g., Survey Present Data E.g., Tables and graphs Characterize Data E.g., Sample Mean =

Inferential Statistics Estimation E.g., Estimate the population mean weight using the sample mean weight Hypothesis Testing E.g., Test the claim that the population mean weight is 120 pounds Drawing conclusions and/or making decisions concerning a population based on sample results.

Syarat Data yang Baik Obyektif (sesuai keadaan sebenarnya) Representatif (mewakili populasi) Reliabilitas (dapat dipercaya) Tepat waktu (up to date) Relevan (sesuai permasalahan)

Data Sources Data Sources Print or Electronic Observation Survey Experimentation

Types of Data

Types of Sampling Methods Samples Probability Samples Non-Probability Samples (Convenience) Simple Random Stratified Judgement Chunk Cluster Systematic Quota

Probability Sampling Subjects of the Sample are Chosen Based on Known Probabilities Probability Samples Simple Random Systematic Stratified Cluster

Penyajian Data Penyajian Data Kualitatif Penyajian Data Kuantitatif : Diagram Titik Diagram dahan dan daun Histrogam Diagram Pencar

Types of Variables Qualitative Quantitative Discrete Continuous

Types of Variables Quantitative variables measure a numerical quantity on each experimental unit. Discrete if it can assume only a finite or countable number of values. Continuous if it can assume the infinitely many values corresponding to the points on a line interval.

Example A bag of M&M®s contains 25 candies: Raw Data: Statistical Table: m Color Tally Frequency Relative Frequency Percent Red 5 5/25 = .20 20% Blue 3 3/25 = .12 12% Green 2 2/25 = .08 8% Orange Brown 8 8/25 = .32 32% Yellow 4 4/25 = .16 16% m m m m m m m m m m m m m m m m m m m m m m m m m

Graphs Bar Chart: Pie Chart: How often a particular category was observed Pie Chart: How the measurements are distributed among the categories

Graphing Quantitative Variables A single quantitative variable measured for different population segments or for different categories of classification can be graphed using a pie or bar chart. A Big Mac hamburger costs $3.64 in Switzerland, $2.44 in the U.S. and $1.10 in South Africa.

Age Tally Frequency Relative Frequency Percent 25 to < 33 1111 5 5/50 = .10 10% 33 to < 41 1111 1111 1111 14 14/50 = .28 28% 41 to < 49 1111 1111 111 13 13/50 = .26 26% 49 to < 57 1111 1111 9 9/50 = .18 18% 57 to < 65 1111 11 7 7/50 = .14 14% 65 to < 73 11 2 2/50 = .04 4%

Key Concepts I. How Data Are Generated 1. Experimental units, variables, measurements 2. Samples and populations 3. Univariate, bivariate, and multivariate data II. Types of Variables 1. Qualitative or categorical 2. Quantitative a. Discrete b. Continuous III. Graphs for Univariate Data Distributions 1. Qualitative or categorical data a. Pie charts b. Bar charts

Organizing Numerical Data 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions Ordered Array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 2 144677 3 028 4 1 Ogive Histograms Stem and Leaf Display Tables Polygons

Tabulating and Graphing Numerical Data 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 Frequency Distributions Cumulative Distributions Ordered Array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 2 144677 3 028 4 1 Ogive Histograms Stem and Leaf Display Tables Polygons

Distribusi frekuensi : Langkah membuat tabel frekuensi Urutkan data mentah dari nilai terkecil ke nilai tertinggi 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Periksa dalam urutan berapa kali muncul Tentukan jumlah kelas (biasanya 5 – 15) Interval kelas ( (nilai maks – nilai min)/k ) 58 - 12 = 46/5 = 10 Tentukan batas kelas (Limits):10, 20, 30, 40, 50, 60 Hitung titik tengah kelas : 15, 25, 35, 45, 55 Buat tabel frekuensi

Distribusi Frekuensi, Frekuensi Relative Frekuensi Distribusi & Percentase Distribusi Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Frequency Percentage Class Frequency 10 but under 20 3 .15 15 20 but under 30 6 .30 30 30 but under 40 5 .25 25 40 but under 50 4 .20 20 50 but under 60 2 .10 10 Total 20 1 100

Penyajian Gambar Distribusi Frekuensi Histogram : Visual dalam bentuk diagram blok Poligon Frekuensi : Visual dalam bentuk grafik Kurva frekuensi : Frekuensi relatif atau persentase disebut Poligon frekuensi relatif atau disebut saja sebagai Poligon persentase. Poligon frekuensi kumulatif atau ogif

Histogram Data in Ordered Array: No Gaps Between Bars Class Boundaries 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 No Gaps Between Bars Class Boundaries Class Midpoints

Poligon Frekuensi Data in Ordered Array: Class Midpoints 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class Midpoints

Tabulating Numerical Data: Cumulative Frequency Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Lower Cumulative Cumulative Limit Frequency % Frequency 10 0 0 20 3 15 30 9 45 40 14 70 50 18 90 60 20 100

Graphing Numerical Data: The Ogive (Cumulative % Polygon) Data in Ordered Array : 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class Boundaries (Not Midpoints)

Pie Chart (for an Investor’s Portfolio) Amount Invested in K$ Savings 15% Stocks 42% CD 14% Percentages are rounded to the nearest percent Bonds 29%

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