MTH 161: Introduction To Statistics

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

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

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)

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.

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

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

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

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

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.

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.

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

15. Simple Bar Chart for Qualitative Data Party Affiliation Example: Bar Charts for Party Affiliation Example

16. Simple Bar Chart for Qualitative Data Party Affiliation Example: Relative Frequency Distribution

17. Simple Bar Chart for Qualitative Data Party Affiliation Example: Relative Frequency Distribution

18. Multiple Bar Chart 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:

19. Multiple Bar Charts Example (Area and Production of Cotton):

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:

21. Component Bar Chart Students’ Enrollment Data

22. 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 Qualitative Data Example: Represent the expenditures on various items of a family by a pie chart.

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

25. 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

26. 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.

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

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