1. 1 Pertemuan 02 Penyajian Data dan Distribusi Frekuensi Matakuliah: I0134 – Metode Statistika Tahun: 2007

2. 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menjelaskan ukuran pemusatan, penyebaran dan data pencilan.

3. 3 Outline Materi Penyajian Data Kualitatif Penyajian Data Kuantitatif : –Diagram Titik –Diagram dahan dan daun –Histrogam –Diagram Pencar

4. 4 Types of Variables Qualitative Quantitative Discrete Continuous

5. 5 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.

6. 6 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

7. 7 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

8. 8 Graphs Bar Chart: How often a particular category was observed Pie Chart: How the measurements are distributed among the categories

9. 9 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.

10. 10 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, 6 45674567 Applet

11. 11 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.

12. 12 Example The prices ($) of 18 brands of walking shoes: 907070707570656860 747095757068654065 40 5 65 8 0 8 5 5 70 0 0 5 0 4 0 5 0 8 90 5 40 5 60 5 5 5 8 8 70 0 0 0 0 0 4 5 5 8 90 5 Reorder

13. 13 Interpreting Graphs: Location and Spread Where is the data centered on the horizontal axis, and how does it spread out from the center?

14. 14 AgeTallyFrequencyRelative Frequency Percent 25 to < 33111155/50 =.1010% 33 to < 411111 1111 11111414/50 =.2828% 41 to < 491111 1111 1111313/50 =.2626% 49 to < 571111 99/50 =.1818% 57 to < 651111 1177/50 =.1414% 65 to < 731122/50 =.044%

15. 15 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

16. 16 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

17. 17 Selamat Belajar Semoga Sukses.