1. Lecture 03 Dr. MUMTAZ AHMED MTH 161: Introduction To Statistics

2. Review of Previous Lecture Methods of Data Presentations Classification of Data Bases of Classification Types of Classifications Tabulation of Data Types of Tabulations Constructing a Statistical Table General Rules of Tabulation Table of frequency distributions Frequency Distribution Relative frequency distribution Cumulative frequency distribution 2

3. Objectives of Current Lecture Graphical Methods of Data Presentations Graphs for qualitative data Bar Charts Simple Bar Chart Multiple Bar Chart Component Bar Chart Pie Charts Graphs for quantitative data Histograms Frequency Polygon Cumulative Frequency Polygon (Frequency Ogive) 3

4. Review: Stem and Leaf Plot Disadvantage of Frequency Table: An obvious disadvantage of using frequency table is that the identity of individual observation is lost in the grouping process. Stem and Leaf plot provides the solution by offering a quick and clear way of sorting and displaying data simultaneously. 4

5. Review: Stem and Leaf Plot METHOD: Sort the data series Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves) e.g. In 13, the leading digit (stem) is 1 and trailing digit (leaf) is 3 and in 21, the leading digit (stem) is 2 and trailing digit (leaf) is 1. List all stems in a column from low to high For each stem, list all associated leaves 5

6. Review: Stem and Leaf Plot Example 1: Consider the temperature data example. The sorted data from low to high is shown below: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Here, use the 10’s digit for the stem unit: 13 is shown as 21 is shown as 35 is shown as 6 StemLeaf 13 21 35

7. Review: Stem and Leaf Plot Sorted data is:12, 13, 17, 21, 24, 24, 26, 27, 28, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Completed Stem-and-leaf diagram 7 StemLeaf 12 3 7 21 4 4 6 7 8 30 2 5 7 8 41 3 4 6 53 8

8. Back-To-Back Stem and Leaf Plot A back-to-back stem and leaf plot is sometimes used to compare two sets of data or rounded and truncated values of the same data. In a back-to-back plot, the same stem is used for the leaves of both plots. Note: Data with more than two digits can be rounded to two digits before plotting or can be truncated to two digits. To truncate means to cut off. For a stem and leaf plot, you would truncate everything after the second digit The number 355 would round to 36 The number 355 would truncate to 35 8

9. Back-To-Back Stem and Leaf Plot Example: The enrollments of eight colleges are listed below. Make a back-to-back stem and leaf plot of enrollments comparing rounded values and truncated values. 9 CollegeEnrollment 11342 21685 31013 42350 53781 61096 71960 83243

10. Back-To-Back Stem and Leaf Plot Step 1: Put data into order. Then round and truncate to two digits. Step 2: Construct Back-to-back stem and leaf plot by using a single stem. 10

11. Graphical Presentation of Data An old saying “a picture is worth a thousand words”. Graph or Chart of a data set often provides the simplest and most efficient display. Common methods for graphically displaying qualitative data : Bar charts Pie charts Common methods for graphically displaying quantitative data : Histogram Frequency Polygon Frequency Ogive

12. Bar Charts for Qualitative Data Most common types of Bar Chart: Simple Bar Chart Multiple Bar Chart Component Bar Chart

13. Simple Bar Chart for Qualitative Data Simple Bar Chart A Simple Bar chart consists of horizontal or vertical bars of equal widths and lengths proportional to the values they represent. It displays graphically the same information concerning qualitative data that a frequency distribution shows in tabular form.

14. Simple Bar Chart for Qualitative Data Party Affiliation Example: Frequency Distribution PartyFrequency (f) PTI10 N9 Q6 P5 Total30

15. Simple Bar Chart for Qualitative Data Party Affiliation Example: Bar Charts for Party Affiliation Example PartyFrequency (f) PTI10 N9 Q6 P5 Total30

16. Simple Bar Chart for Qualitative Data Party Affiliation Example: Relative Frequency Distribution PartyFreq (f)Relative Frequency PTI100.3333 N90.30 Q60.20 P50.1667 Total301

17. Simple Bar Chart for Qualitative Data Party Affiliation Example: Relative Frequency Distribution PartyFreq (f)Relative Frequency PTI100.3333 N90.30 Q60.20 P50.1667 Total301

18. Multiple Bar Chart Multiple Bar Chart shows two or more characteristics corresponding to values of a common variable in the form of a grouped bars, whose lengths are proportional to the values of the characteristics. Example: Draw multiple bar charts to show the area and production of cotton in Punjab for the following data: YearArea (000 acres) Production (000 bales) 1965-6628661588 1970-7132332229 1975-7634201937

19. Multiple Bar Charts Example (Area and Production of Cotton): YearArea (000 acres) Production (000 bales) 1965-6628661588 1970-7132332229 1975-7634201937

20. Component Bar Chart Component Bar Chart (subdivided bars) A bar is divided into two or more sections, proportional in size to the component parts of a total displayed by each bar. Example: Draw component bar chart of the students’ enrollment data: ClassesTotalMaleFemale BBA653332 MBA603228 MS/PHD402119

21. Component Bar Chart Students’ Enrollment Students’ Enrollment Data ClassesTotalMaleFemale BBA653332 MBA603228 MS/PHD402119

22. Pie Charts For Pie Charts For Qualitative Data A Pie-Chart (also called sector diagram), is a graph consisting of a circle divided into sectors whose areas are proportional to the various parts into which whole quantity is divided.

23. Pie Charts For Pie Charts For Qualitative Data Example: Represent the expenditures on various items of a family by a pie chart. ItemsExpenditure (in 100 rupees) Food50 Clothing30 Rent20 Fuel15 Misc.35 Total150

24. Pie Charts For Pie Charts For Qualitative Data Steps for Constructing Pie-Chart: Step 1: Draw a circle of any radius

25. Pie Charts For Pie Charts For Qualitative Data Steps for Constructing Pie-Chart: Step 2: Find angle of each sector corresponding to share of each component. Angle of sector=(component part/whole quantity) * 360 ItemsExpenditure (in 100 rupees)Angles of sector (in Degrees) Food50 (50/150)*360=120 0 Clothing30 (30/150)*360=72 0 Rent20 (20/150)*360=48 0 Fuel15 (15/150)*360=36 0 Misc.35 (35/150)*360=84 0 Total150360 0

26. Pie Charts For Pie Charts For Qualitative Data Steps for Constructing Pie-Chart: Step 3: Divide the circle into various sectors by measuring the corresponding angle via protector. ItemsExpenditure (in 100 rupees) Angles of sector (in Degrees) Food50 120 0 Clothing30 72 0 Rent20 48 0 Fuel15 36 0 Misc.35 84 0 Total150360 0

27. Review Let’s review the main concepts: Graphical Methods of Data Presentations Graphs for qualitative data Bar Charts Simple Bar Chart Multiple Bar Chart Component Bar Chart Pie Charts 27

28. Next Lecture In next lecture, we will study: Graphs for quantitative data Histograms Frequency Polygon Cumulative Frequency Polygon (Frequency Ogive) 28