1 Pertemuan 01 Pendahuluan Matakuliah: I Statistika Tahun: 2008 Versi: Revisi

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menjelaskan tentang statistika, data, populasi, sampel, variabel, penyajian data, dan skala pengukuran.

3 Outline Materi Definisi statistika Jenis-jenis Data Pengumpulan dan Penyajian Data Teknik Sampling Distribusi Frekuensi Skala pengukuran

4 What is Statistics? Analysis of data (in short) Design experiments and data collection Summary information from collected data Draw conclusions from data and make decision based on finding

5 Design of Survey Research Choose an Appropriate Mode of Response –Reliable primary modes Personal interview Telephone interview Mail survey –Less reliable self-selection modes (not appropriate for making inferences about the population) Television survey Internet survey Printed survey in newspapers and magazines Product or service questionnaires

6 Reasons for Drawing a Sample Less Time Consuming Than a Census Less Costly to Administer Than a Census Less Cumbersome and More Practical to Administer Than a Census of the Targeted Population

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

8 Probability Sampling Subjects of the Sample are Chosen Based on Known Probabilities Probability Samples Simple Random SystematicStratifiedCluster

9 Variables and Data variableA variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration. Examples:Examples: –Body temperature is variable over time or (and) from person to person. –Hair color, white blood cell count, time to failure of a computer component.

10 Definitions experimental unitAn experimental unit is the individual or object on which a variable is measured. measurementA measurement results when a variable is actually measured on an experimental unit. data, sample population.A set of measurements, called data, can be either a sample or a population.

11 Example Variable – Hair color Experimental unit –Person Typical Measurements –Brown, black, blonde, etc.

12 How many variables have you measured? Univariate data:Univariate data: One variable is measured on a single experimental unit. Bivariate data:Bivariate data: Two variables are measured on a single experimental unit. Multivariate data:Multivariate data: More than two variables are measured on a single experimental unit.

13 Types of Variables Qualitative Quantitative Discrete Continuous

14 Types of Variables Qualitative variablesQualitative variables measure a quality or characteristic on each experimental unit. (Categorical Data) Examples:Examples: Hair color (black, brown, blonde…) Make of car (Dodge, Honda, Ford…) Gender (male, female) State of birth (California, Arizona,….)

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

16 Examples For each orange tree in a grove, the number of oranges is measured. –Quantitative discrete For a particular day, the number of cars entering a college campus is measured. –Quantitative discrete Time until a light bulb burns out –Quantitative continuous

17 Graphing Qualitative Variables data distributionUse a data distribution to describe: –What values –What values of the variable have been measured –How often –How often each value has occurred “ How often ” can be measured 3 ways: –Frequency in each category –Relative frequency = Frequency/n (proportion in each category) –Percent = 100 x Relative frequency

18 Example A bag of M&M ® s contains 25 candies: Raw Data:Raw Data: Statistical Table:Statistical Table: ColorTallyFrequencyRelative Frequency Percent Red55/25 =.2020% Blue33/25 =.1212% Green22/25 =.088% Orange33/25 =.1212% Brown88/25 =.3232% Yellow44/25 =.1616% m m m mm 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 m mmmm mm m mm mmmmmmm mmm

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

20 Graphing Quantitative Variables pie bar chartA 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.

21 Dotplots The simplest graph for quantitative data Plots the measurements as points on a horizontal axis, stacking the points that duplicate existing points. Example:Example: The set 4, 5, 5, 7, Applet

22 Stem and Leaf Plots A simple graph for quantitative data Uses the actual numerical values of each data point. –Divide each measurement into two parts: the stem and the leaf. –List the stems in a column, with a vertical line to their right. –For each measurement, record the leaf portion in the same row as its matching stem. –Order the leaves from lowest to highest in each stem. –Provide a key to your coding. –Divide each measurement into two parts: the stem and the leaf. –List the stems in a column, with a vertical line to their right. –For each measurement, record the leaf portion in the same row as its matching stem. –Order the leaves from lowest to highest in each stem. –Provide a key to your coding.

23 Example The prices ($) of 18 brands of walking shoes: Reorder

24 Interpreting Graphs: Location and Spread Where is the data centered on the horizontal axis, and how does it spread out from the center?

25 Tabulating and Graphing Numerical Data Numerical Data Ordered Array Stem and Leaf Display Histograms Ogive Tables , 24, 32, 26, 27, 27, 30, 24, 38, 21 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Frequency Distributions Cumulative Distributions Polygons

26 Tabulating Numerical Data: Frequency Distributions Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Find range: = 46 Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits): 10, 20, 30, 40, 50, 60 Compute class midpoints: 15, 25, 35, 45, 55 Count observations & assign to classes

27 Frequency Distributions, Relative Frequency Distributions and Percentage Distributions Class Frequency 10 but under but under but under but under but under Total Relative Frequency Percentage Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

28 Graphing Numerical Data: The Histogram Data in ordered array: 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 Midpoints Class Boundaries

29 Graphing Numerical Data: The Frequency Polygon Class Midpoints Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

30 Tabulating Numerical Data: Cumulative Frequency Cumulative Cumulative Class Frequency % Frequency 10 but under but under but under but under but under Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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

Skala Pengukuran : –Nominal –Ordinal –Interval –Rasio

Karakteristik SkalaPengukuran Skala Penguku ran Pembedaan Kategori Urutan/ Peringkat Jarak Di antara Kategori Nilai Absolut NominalYa--- OrdinalYaYa-- IntervalYaYaYa- RasioYaYaYaYa

34 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

35 Key Concepts 2. Quantitative data a. Pie and bar charts b. Line charts c. Dotplots d. Stem and leaf plots e. Relative frequency histograms 3. Describing data distributions a. Shapes — symmetric, skewed left, skewed right, unimodal, bimodal b. Proportion of measurements in certain intervals c. Outliers

36 Selamat Belajar Semoga Sukses.