LECTURE NO 3.pdf
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Lecture No. 03 Graphical Representation of Data No of slides: 31 1 Graphical Representation of Data Desired Learning Objectives You will be able to Understand the concept of graphs/ diagrams Apply th...
Lecture No. 03 Graphical Representation of Data No of slides: 31 1 Graphical Representation of Data Desired Learning Objectives You will be able to Understand the concept of graphs/ diagrams Apply these techniques in the fields of engineering / AI particularly while conducting technical investigations 2 Graphical Representation of Data Though the data presented in the form of table yields a good information, they are not always good for all Showing data in the form of a graph can make complex and confusing information appear more simple and straightforward Different graphs and charts are used for data representation 3 Graphical Representation of Data Types of Graphical Representation Un-Grouped Data Grouped Data 4 Graphical Representation of Data Types of Graphical Representation Grouped Data Histogram Frequency polygon Cumulative frequency polygon (OGIVE) 5 Graphical Representation of Data Types of Graphical Representation Un-Grouped Data Bar chart Simple bar chart Multiple bar chart Component bar chart Pie chart 6 Graphical Representation of Data HISTOGRAM Histogram is the most common graphical presentation of a frequency distribution for numerical data It uses a series of adjacent bars in which the width of each bar represents the class width and the heights represent the frequency or relative frequency of the class It is used for grouped data in which the class boundaries are marked on the x-axis and the frequencies are marked along the y- axis 7 Graphical Representation of Data Frequency distribution & Histogram Example 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Classes Class Boundaries Frequency 10 – 19 9.5 – 19.5 3 20 – 29 19.5 – 29.5 6 30 – 39 29.5 – 39.5 5 40 – 49 39.5 – 49.5 4 50 – 59 49.5 – 59.5 2 Total 20 8 Graphical Representation of Data Histogram Example His togram 7 6 6 5 Frequency 5 4 4 3 No gaps between 3 2 bars, since 2 continuous data 1 0 0 0 5 15 25 36 45 55 More Class Boundaries 9 Graphical Representation of Data Frequency Polygon It is a graph that consists of line segments connecting the intersection of the class marks and the frequencies of a continuous frequency distribution It can also be constructed from histogram by joining the mid- points of each bar 10 Graphical Representation of Data Frequency Polygon His togram 7 6 6 5 Frequency 5 4 4 3 No gaps between 3 bars, since 2 2 continuous data 1 0 0 0 5 15 25 36 45 55 More Class Midpoints 11 Graphical Representation of Data Frequency Polygon 12 Graphical Representation of Data Cumulative Frequency Distributions (OGIVE) As there are two cumulative frequency distributions, there are two OGIVE (pronounced as “oh-jive”) curves These are the less than cumulative frequency which is a line graph joining the intersection points of the upper class boundaries and their corresponding less than cumulative frequencies And more than cumulative frequency which is a line graph joining the intersection points of the lower class boundaries and their corresponding more than cumulative frequencies 13 Graphical Representation of Data Frequency Distribution Classes Class Boundaries Frequency 65-84 64.5-84.5 9 85-104 84.5-104.5 10 105-124 104.5-124.5 17 125-144 124.5-144.5 10 145-164 144.5-164.5 5 165-184 164.5-184.5 4 185-204 184.5-204.5 5 Total 60 14 Graphical Representation of Data Cumulative Frequency Polygon (OGIVE) Cumulative Weights (grams) Frequency < Less than 64.5 0 Less than 84.5 9 Less than 104.5 19 Less than 124.5 36 Less than 144.5 46 Less than 164.5 51 Less than 184.5 55 Less than 204.5 60 15 Graphical Representation of Data Cumulative Frequency Polygon (OGIVE) Cumulative Weights (grams) Frequency > more than 64.5 60 more than 84.5 51 more than 104.5 41 more than 124.5 24 more than 144.5 14 more than 164.5 9 more than 184.5 5 more than 204.5 0 16 Graphical Representation of Data Cumulative Frequency Polygon (OGIVE) 17 Graphical Representation of Data (Un-grouped Data) Charts / Diagrams Whenever a comparison of the same type of data at different places is to be made, charts also called diagrams will be the best way to do that Beautifully and neatly constructed charts are more attractive 18 Graphical Representation of Data (Un-grouped Data) Types of Charts/ diagrams Simple Bar Chart Multiple Bar Chart Component Bar Chart Pie Chart 19 Graphical Representation of Data (Un-grouped Data) Simple Bar Diagram Consists of horizontal or vertical bars of equal widths and lengths proportional to the values they represent 20 Graphical Representation of Data (Un-grouped Data) Simple Bar Diagram Problem: Draw a simple bar diagram to represent the turnover of a company for 5 years Years 1965 1966 1967 1968 1969 Turnover 35000 42000 43500 48000 48500 (rupees) 21 Graphical Representation of Data (Un-grouped Data) Simple Bar Diagram 22 Graphical Representation of Data (Un-grouped Data) Multiple Bar Diagram It shows two or more characteristics corresponding to the values of a common variable in the form of grouped bars, whose lengths are proportional to the values of the characteristics, and each of which is shaded differently to be identified 23 Graphical Representation of Data (Un-grouped Data) Multiple Bar Diagram Problem Draw multiple bar diagram to show the areas and production of cotton in the Punjab from the following data Years 1965-66 1970-71 1975-76 Area (acre) 2866 3233 3420 Production 1588 2229 1937 24 Graphical Representation of Data (Un-grouped Data) Multiple Bar Diagram 25 Graphical Representation of Data (Un-grouped Data) Component Bar Diagram Each bar is divided into two or more sections, proportional in size to the component parts of a total being displayed by each bar. These parts are then shaded differently to be identified 26 Graphical Representation of Data (Un-grouped Data) Component Bar Diagram Problem Draw a component bar diagram for the following data Divisions Peshawar Rawalpindi Sargodha Lahore 64 40 60 65 Males 33 21 32 35 Females 31 19 28 30 27 Graphical Representation of Data (Un-grouped Data) Component Bar Diagram 28 Graphical Representation of Data (Un-grouped Data) Pie-Chart It is also known as sector diagram. It is a graphic device consisting of a circle divided into sectors or pie-shaped pieces whose areas are proportional to the various parts into which the whole quantity is divided 29 Graphical Representation of Data (Un-grouped Data) Pie-Chart Construction steps Find percentage of each category (share / total )*100 Find angle share of each category (share/total)*360 30 Example Suppose we are carrying out a survey of the students of 1st year studying in a co-educational college of Lahore. Suppose that in all there are 1200 students of first year in this large college. We wish to determine what proportions of of these students have come from Urdu medium schools and what proportion has come from English medium schools? Data collected is as No of Students Medium of Instruction (f) Urdu 719 English 481 Total 1200 31 Solution Dividing the cell frequencies by the total frequency and multiplying by 100 we obtain the following No of Students Medium of Instruction % (f) Urdu 719 59.9 =60% English 481 40.1 =40% Total 1200 A pie chart consists of a circle which is divided into two or more parts in accordance with the number of distinct categories that we have in our data 32 Graphical Representation of Data (Un-grouped Data) The circle is divided into two sectors, the larger sector pertaining to students coming from Urdu medium schools and the smaller sector pertaining to students coming from English medium schools How do we decide where to cut the circle? The answer is very simple! All we have to do is to divide the cell frequency by the total frequency and multiply by 360. This process will give us the exact value of the angle at which we should cut the circle 33 Pie Chart No of Students Medium of Instruction Angle (f) Urdu 719 English 481 Total 1200 English 40% Urdu Urdu 60% English 34 Questions for Practice Assignment-2 35 Graphical Representation of Data (Un-grouped Data) Represent the total expenditure and expenditures on various items of a family by a pie diagram Food Clothing HR Fuel Misc Expenditure 50 30 20 15 35 36 Graphical Representation of Data (Un-grouped Data) Draw a component bar diagram for the following data Net users Mon Tues Wed Thrs Fri per day 100 140 60 265 131 Server 1 33 100 21 132 35 Server 2 31 10 09 78 55 Server 3 36 30 30 55 41 37 Cumulative Lower Limit Upper Limit Count Count 29.5 39.5 0 0 39.5 49.5 3 3 49.5 59.5 10 13 59.5 69.5 53 66 69.5 79.5 107 173 79.5 89.5 147 320 89.5 99.5 130 450 Draw Histogram using given data also find frequency polygon and cumulative frequency polygon for the given data as well 38
