Introduction To Statistics

Lecture 03

Dr. MUMTAZ AHMEDMTH 161: Introduction To StatisticsReview of Previous LectureMethods of Data PresentationsClassification of DataBases of ClassificationTypes of ClassificationsTabulation of DataTypes of TabulationsConstructing a Statistical TableGeneral Rules of TabulationTable of frequency distributionsFrequency DistributionRelative frequency distributionCumulative frequency distribution22Objectives of Current LectureGraphical Methods of Data PresentationsGraphs for qualitative dataBar ChartsSimple Bar ChartMultiple Bar ChartComponent Bar ChartPie ChartsGraphs for quantitative dataHistogramsFrequency PolygonCumulative Frequency Polygon (Frequency Ogive)33Review: Stem and Leaf PlotDisadvantage 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.4Review: Stem and Leaf PlotMETHOD:Sort the data seriesSeparate 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 highFor each stem, list all associated leaves

5Review: Stem and Leaf PlotExample 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, 58Here, use the 10s digit for the stem unit:

13 is shown as21 is shown as35 is shown as

6StemLeaf132135Review: Stem and Leaf PlotSorted 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

7StemLeaf12 3 721 4 4 6 7 830 2 5 7 841 3 4 6 53 8Back-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 digitThe number 355 would round to 36 The number 355 would truncate to 35

8Back-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.9CollegeEnrollment1134221685310134235053781610967196083243Back-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

Graphical Presentation of DataAn 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 chartsPie chartsCommon methods for graphically displaying quantitative data :HistogramFrequency PolygonFrequency Ogive

Bar Charts for Qualitative DataMost common types of Bar Chart:

Simple Bar ChartMultiple Bar ChartComponent Bar ChartSimple Bar Chart for Qualitative DataSimple Bar ChartA 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.

Simple Bar Chart for Qualitative DataParty Affiliation Example:

Frequency DistributionPartyFrequency (f)PTI10N9Q6P5Total30Simple Bar Chart for Qualitative DataParty Affiliation Example:

Bar Charts for Party Affiliation ExamplePartyFrequency (f)PTI10N9Q6P5Total30Simple Bar Chart for Qualitative DataParty Affiliation Example:

Relative Frequency DistributionPartyFreq (f)Relative FrequencyPTI100.3333N90.30Q60.20P50.1667Total301Simple Bar Chart for Qualitative DataParty Affiliation Example:

Relative Frequency DistributionPartyFreq (f)Relative FrequencyPTI100.3333N90.30Q60.20P50.1667Total301Multiple Bar ChartMultiple Bar ChartMultiple 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)1965-66286615881970-71323322291975-7634201937Multiple Bar ChartsExample (Area and Production of Cotton):YearArea (000 acres)Production (000 bales)1965-66286615881970-71323322291975-7634201937Component Bar ChartComponent 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:

ClassesTotalMaleFemaleBBA653332MBA603228MS/PHD402119Component Bar ChartStudents Enrollment DataClassesTotalMaleFemaleBBA653332MBA603228MS/PHD402119Pie Charts For Qualitative DataA 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.Pie Charts For Qualitative DataExample: Represent the expenditures on various items of a family by a pie chart.

ItemsExpenditure (in 100 rupees)Food50Clothing30Rent20Fuel15Misc.35Total150Pie Charts For Qualitative DataSteps for Constructing Pie-Chart:Step 1: Draw a circle of any radiusPie Charts For Qualitative DataSteps 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=1200Clothing30(30/150)*360=720Rent20(20/150)*360=480Fuel15(15/150)*360=360Misc.35(35/150)*360=840Total1503600Pie Charts For Qualitative DataSteps 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)Food501200Clothing30720Rent20480Fuel15360Misc.35840Total1503600ReviewLets review the main concepts:

Graphical Methods of Data PresentationsGraphs for qualitative dataBar ChartsSimple Bar ChartMultiple Bar ChartComponent Bar ChartPie Charts27Next LectureIn next lecture, we will study:Graphs for quantitative dataHistogramsFrequency PolygonCumulative Frequency Polygon (Frequency Ogive)28