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Methods for Presentation of Data

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### Social statistics

1. 1. THE UNIVERSITY OF AZAD JAMMU & KASHMIR MUZAFFARABAD Social Statistics Assignment No. 01 Submitted to: Sir Atif Abbasi Submitted by: Waheed Ahmad Qureshi Roll No. 67 Page 1 of 15
2. 2. Q. No.1: Discuss the different methods for the presentation of Data with Examples.Methods for the Presentation of DataIntroduction:Data may be collected through different sources. It is difficult to learn anything by examiningthe un-organized data which is more often confusing than clarifying. The mass of data istherefore to be organized and condensed into a form that can be easily understood andinterpreted. For this purpose techniques of classification, tabulation and graphic displays areintroduced.Data:Data is the collection of facts from which the conclusion may be drawn. It is further classifiedinto two types: 1. Primary Data 2. Secondary DataPresentation of Data:The methods which are used for the presentation of data are as under: 1. Classification 2. Tabulation 3. Graphical Representation 4. Diagrammatic Representation1. CLASSIFICATION: One of the methods of the Presentation of data is classification. It is a process of dividing a set of observations or objects into classes or groups in such a way that: i. Observations or objects in the same class or group are similar. ii. Observations or objects in each class or group are dissimilar to the other groups. Definition: “The process of arranging data into classes or categories according to some common characteristics present in the data is called classification”. e.g. attributes, weights, geographical characteristics etc. Examples: i. The population of country may be classified by religion as Muslim, Christians, and Hindus etc. ii. If in a primary school examination, we have the results of 1000 students, it is difficult to tell. Similarly, by looking at the marks, as how many Page 2 of 15
3. 3. students obtained marks from 350 to 449, 450 to 549, 550 to 659 and so on. Now if we arrange the data and make the groups and find out number of students in each group. It is easy to understand. Basis of classification: Although data can be classified by many characteristics but there are four important basis for classification of data Qualitative: When data are classified by attributes, e.g., sex, religion,, martial status, morality, friendship etc. Quantitative: When data are classified by quantitative characteristics, e.g., heights, weights, age, speed etc Spatial or Geographical: When data are classified by geographical region or location e.g., the population of a country may be classified by provinces, divisions, districts or towns Chronological or Temporal: When data are classified by their time of occurrence such arrangement is called a time series. Basic principals of classification: While classifying large sets of data, the following points should be taken into consideration • The classes or categories, into which the data are to be divided, should be mutually exclusive and no overlap should exist between successive classes. In other words, classes should be arranged so that each observation or object can be placed in one and only one class. • The classes or categories should be all inclusive. All inclusive classes are classes that include all the data. • As far as possible, the conventional classification procedure should be adopted. • The classification procedure should not be so elaborate as to lead to trivial classes nor should it be so crude as to concentrate all the data in one or two classes.2. TABULATION: Statistical table is a systematic arrangement of data into vertical columns and horizontal rows. The process of arranging data into rows and columns is called tabulation. According to Prof. Bowely, “Tabulation is the intermediate process between the accumulations of data, in whatever form they are obtained and the final accounts of the results shown by the statistics”. Page 3 of 15
4. 4. Tabulation may be: Simple When tabulation is done according to one way classification, like the population of a country is classified according to religion or marital status, called simple classification. Double When tabulation corresponding to two way classification, such as tabulation of data classified by religion and sex or religion and material status is an example of double tabulation. Complex When tabulation is done by many-way classification, it is called complex tabulation. An example of complex tabulation is the presentation of data on the population of a country classified by age, sex, religion and marital status etc. Main Parts of Table: As statistical table has at least four parts – the title, stub, head and body. In addition, some tables have one or more prefatory notes, a foot note and a source note. All these are shown in the following Table: Population of Punjab and Baluchistan provinces by sex for 1961 and 1972 censuses1 Punjab Baluchistan Census Male Female Total Male Female Total 1961 1364 19938 2558 640 521 1161 3 1 1972 1994 17566 3750 1272 1133 2405 2 8 A description of there parts are given below: Title: Every table must have title; it should be brief, clearly worded and self explanatory. The title should describe a. what the data represents b. where the data come from c. how the data have been classified d. where the data were observed Column, Captions and Box Head The heading of a column is called a column caption and the section or parts of the table containing the column caption is known as box head. The captions should clearly defined and written in the centre of the columns. Row Captions and Stub1 Population census reports, 1961 and 1972 Page 4 of 15
5. 5. The heading or title of a row is called the row caption and the section of the table containing row captions is known as stub. Prefatory Notes and Foot Notes Both these notes are used to explain certain characteristics of the data. They give additional specification of the data. a. The prefatory notes appear between the title and the body. b. A foot note appears immediately below the body of the table.3. GRAPHICAL REPRESENTATION Visual display of statistical data in the form of points, lines, areas and other geometrical forms and symbols is the most general term known as graphical representation of data. Statistical data can be studies with this method without going through figures presented in the form of tables. Graph It is in the form of continuous curve, shown on a graph paper. Diagram It Is in the form of one, two or three dimensional or in pictorial form. Types of diagrams or charts Following types of diagrams are in common use One dimensional diagrams or charts These diagrams have only one dimension. They are used to represent data not having large variations. It consists of • Simple bar diagram or chart. • Multiple bar diagram or chart • Sub divided bar diagram or component chart. Simple Bar Diagram or Chart This chart consists of vertical or horizontal bars of equal width. The length of bars is taken proportional to the magnitude of the values presented. Example Draw simple bar chart to represent the production of wheat in Pakistan during the years 1971 to 1976 Page 5 of 15
6. 6. Year 1971 1972 1973 1974 1975 1976 Production 55 60 72 69 69 72 (lake tons) lakh tons 80 70 60 50 wheat 40 30 20 10 0 1971 1972 1973 1974 1975 1976Simple bar chart showing production of wheat in Pakistan for the years 1971 to 1976Multiple Bar ChartsIt is an extension of simple bar chart. In this chart grouped bars are used to representrelated set of data. For example, we may represent the imports of a country for anumber of years by means of multiple bars chart, taking groups of 2 bars each--- onerepresenting imports and the other representing exports. Each bar in a group is shadedor colored differentially for distinction. Similarly it may have more than 2 groups ofdataExample; draw a multiple bar chart to represent the imports and exports of Pakistan(value in crores of rupees ) for the year 1970-71 to 1974-75 Years Imports Exports 1970-1971 370 200 1971-1972 350 337 1972-1973 840 855 1973-1974 1438 1016 1974-1975 2092 1029 Source: state bank of Pakistan Page 6 of 15
7. 7. 2500 2000 1500 Imports Exports 1000 500 0 1970-1971 1971-1972 1972-1973 1973-1974 1974-1975Multiple bar chart showing Imports and Exports of Pakistan from 1970-71 to 1974-75Sub Divided or Component Bar ChartThis chart is used when it is desired to present data which are subdivisions of totals.Since the bars show the various component parts, it is also called component barcharts. In this charts simple bars are drawn with lengths proportion to the totals andthen sub divided in to the parts in the ratio of their components. The components orshaded or colored differentially so as to distinguish differ parts.Example: Draw sub divided bar diagram to represent the male and female populationof five divisions of Pakistan in 1961. Division Male Female Both Sexes Bahawalpur 14 12 26 Rawalpindi 21 19 40 Sargodha 32 28 60 Lahore 35 30 65 Multan 35 31 66Source: Population census Report, 1961. Page 7 of 15
8. 8. 70 60 50 40 Female Male 30 20 10 0 1 2 3 4 5Sub-divided bar graph showing male & female population of five divisions ofPakistan in 1961Pie chartsLike the rectangles, circles can also be used to represent and compare data havinglarge variation. Circles are drawn with radius proportional to the square roots ofquantities to be represented (because the area of a circle is given by 2πr2). Circles aresub divided into sectors when the totals and their sub divisions have to be compares.The sectors are shaded or colored differentially. This diagram is used for the samepurpose as the sub divided rectangles however it is difficult to compare areas visually.For this reason this an inferior form of presentation. The titles describing eachcomponent part should be written in each sector.To construct a pie chart draw a circle with some suitable radius we know that a circleconsists of 360°. To show the components pair by sectors we calculate the angles foreach sectors by the formula.The circle is divided in to different sectors by constructing angles at the centre bymeans of a protractor. The arrangement of the sectors is generally clock wise.Example: Draw a pie chart to show the distribution Page 8 of 15
9. 9. Academic Number of Cumulative Angles of sectors qualification Employees Angles No Education 47 (47/296) x 360°= 57° 57° Primary 25 (25/296) x 360°= 30° 87° Middle 63 77° 164° Matric 97 118° 282° Intermediate 26 32° 314° Bachelor 23 28° 342° Master 15 18° 360° Total 296 360Sources: Census of Punjab government Employees Punjab Government Employees by Academic Qualification No Education Primary Middle Matric Intermediate Bachclor’s Degree Master’s DegreeGraphs:As we know, the diagrams are useful for representing spatial series. Diagrams failwhen we want to represent a statistical series spread over a period of time, or afrequency distribution or two related variables in visual form. For suchrepresentations, graphs are employed.Graphs present the data in a simple, clear and effective manner, facilitate comparisonbetween two or more than two statistical series and help us in appreciating theirsignificance readily. Graphs can be divided into two main categories, namely: i. Graph of time series ii. Graphs of frequency distribution Page 9 of 15
10. 10. Example:Draw a histogram to represent production of cigarettes in Pakistan for the year 1959to 1968 1959- 1960- 1961- 1962- 1964- 1965- 1966- 1967- 1968- Year 60 61 62 63 65 66 67 68 69 Production 928 1088 1326 1456 1767 1984 2445 3205 3493 4000 3500 3000 2500 2000 1500 1000 500 0 1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68A histogram consists of a set of adjacent rectangles having bases along the X-axis(marked off by class boundaries) and areas proportional to the class frequencies. If theclass interval sizes, are equal the heights of the rectangles are also proportional to theclass frequencies if the class interval sizes are not equal, then the heights of therectangles have to be adjusted.Histogram for Frequency Distribution of Annual Death Rates Class Boundaries Frequency 3.45 – 4.45 1 4.45 – 5.45 4 5.45 – 6.45 5 6.45 – 7.45 13 7.45 – 8.45 12 8.45 – 9.45 19 9.45 – 20.45 13 10.45 – 11.45 10 11.45 – 12.45 6 12.45 – 13.45 4 13.45 – 14.45 1 Page 10 of 15
11. 11. Academic Number of Cumulative Angles of sectors qualification Employees Angles No Education 47 (47/296) x 360°= 57° 57° Primary 25 (25/296) x 360°= 30° 87° Middle 63 77° 164° Matric 97 118° 282° Intermediate 26 32° 314° Bachelor 23 28° 342° Master 15 18° 360° Total 296 360Sources: Census of Punjab government Employees Punjab Government Employees by Academic Qualification No Education Primary Middle Matric Intermediate Bachclor’s Degree Master’s DegreeGraphs:As we know, the diagrams are useful for representing spatial series. Diagrams failwhen we want to represent a statistical series spread over a period of time, or afrequency distribution or two related variables in visual form. For suchrepresentations, graphs are employed.Graphs present the data in a simple, clear and effective manner, facilitate comparisonbetween two or more than two statistical series and help us in appreciating theirsignificance readily. Graphs can be divided into two main categories, namely: i. Graph of time series ii. Graphs of frequency distribution Page 9 of 15