social statistics

THE UNIVERSITY OF AZAD JAMMU & KASHMIRMUZAFFARABAD

Social Statistics

Assignment No. 01

Submitted to:Sir Atif Abbasi

Submitted by:

Waheed Ahmad QureshiRoll No. 67

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Q. No.1: Discuss the different methods for the presentation of Data with Examples.

Methods for the Presentation of Data

Introduction:

Data may be collected through different sources. It is difficult to learn anything by examining the un-organized data which is more often confusing than clarifying. The mass of data is therefore to be organized and condensed into a form that can be easily understood and interpreted. For this purpose techniques of classification, tabulation and graphic displays are introduced.

Data:

Data is the collection of facts from which the conclusion may be drawn. It is further classified into two types:

1. Primary Data2. Secondary Data

Presentation of Data:

The methods which are used for the presentation of data are as under:

1. Classification2. Tabulation3. Graphical Representation4. Diagrammatic Representation

1. 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

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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”.

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Tabulation may be:

SimpleWhen 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.

DoubleWhen 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.

ComplexWhen 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

CensusPunjab Baluchistan

Male Female Total Male Female Total1961 13643 19938 25581 640 521 11611972 19942 17566 37508 1272 1133 2405

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 representsb. where the data come fromc. how the data have been classifiedd. where the data were observed

Column, Captions and Box HeadThe 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 StubThe 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

1 Population census reports, 1961 and 1972

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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.

GraphIt is in the form of continuous curve, shown on a graph paper.

DiagramIt Is in the form of one, two or three dimensional or in pictorial form.

Types of diagrams or chartsFollowing types of diagrams are in common use

One dimensional diagrams or chartsThese 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 ChartThis 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

Year 1971 1972 1973 1974 1975 1976Production (lake tons)

55 60 72 69 69 72

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Simple bar chart showing production of wheat in Pakistan for the years 1971 to 1976

Multiple Bar Charts

It is an extension of simple bar chart. In this chart grouped bars are used to represent related set of data. For example, we may represent the imports of a country for a number of years by means of multiple bars chart, taking groups of 2 bars each--- one representing imports and the other representing exports. Each bar in a group is shaded or colored differentially for distinction. Similarly it may have more than 2 groups of data

Example; 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 Exports1970-19711971-19721972-19731973-19741974-1975

37035084014382092

20033785510161029

Source: state bank of Pakistan

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0

500

1000

1500

2000

2500

1970-1971 1971-1972 1972-1973 1973-1974 1974-1975

Imports

Exports

Multiple bar chart showing Imports and Exports of Pakistan from 1970-71 to 1974-75

Sub Divided or Component Bar Chart

This 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 bar charts. In this charts simple bars are drawn with lengths proportion to the totals and then sub divided in to the parts in the ratio of their components. The components or shaded or colored differentially so as to distinguish differ parts.

Example: Draw sub divided bar diagram to represent the male and female population of five divisions of Pakistan in 1961.

Division Male Female Both SexesBahawalpurRawalpindiSargodhaLahoreMultan

1421323535

1219283031

2640606566

Source: Population census Report, 1961.

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0

10

20

30

40

50

60

70

1 2 3 4 5

Female

Male

Sub-divided bar graph showing male & female population of five divisions of Pakistan in 1961

Pie charts

Like the rectangles, circles can also be used to represent and compare data having large variation. Circles are drawn with radius proportional to the square roots of quantities to be represented (because the area of a circle is given by 2πr2). Circles are sub 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 same purpose 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 each component part should be written in each sector.

To construct a pie chart draw a circle with some suitable radius we know that a circle consists of 360°. To show the components pair by sectors we calculate the angles for each sectors by the formula.

The circle is divided in to different sectors by constructing angles at the centre by means of a protractor. The arrangement of the sectors is generally clock wise.

Example: Draw a pie chart to show the distribution

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Academic qualification

Number ofEmployees

Angles of sectorsCumulative

AnglesNo Education

PrimaryMiddleMatric

IntermediateBachelorMaster

47256397262315

(47/296) x 360°= 57°(25/296) x 360°= 30°

77°118°32°28°18°

57°87°164°282°314°342°360°

Total 296 360

Sources: Census of Punjab government Employees

Graphs:

As we know, the diagrams are useful for representing spatial series. Diagrams fail when we want to represent a statistical series spread over a period of time, or a frequency distribution or two related variables in visual form. For such representations, graphs are employed.

Graphs present the data in a simple, clear and effective manner, facilitate comparison between two or more than two statistical series and help us in appreciating their significance readily. Graphs can be divided into two main categories, namely:

i. Graph of time series

ii. Graphs of frequency distribution

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0

500

1000

1500

2000

2500

3000

3500

4000

1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68

Example:

Draw a histogram to represent production of cigarettes in Pakistan for the year 1959 to 1968

Year1959-

601960-

611961-

621962-

631964-

651965-

661966-

671967-

681968-

69

Production 928 1088 1326 1456 1767 1984 2445 3205 3493

A 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 the class interval sizes, are equal the heights of the rectangles are also proportional to the class frequencies if the class interval sizes are not equal, then the heights of the rectangles have to be adjusted.

Histogram for Frequency Distribution of Annual Death Rates

Class Boundaries Frequency3.45 – 4.454.45 – 5.455.45 – 6.456.45 – 7.457.45 – 8.458.45 – 9.459.45 – 20.4510.45 – 11.4511.45 – 12.4512.45 – 13.4513.45 – 14.45

1451312191310641

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0

2

4

6

8

10

12

14

16

18

20

Frequency Polygon and Frequency Curve

Frequency polygon

A frequency polygon is a graph of a frequency distribution. It is constructed by plotting the class frequencies against their corresponding class marks (mid points) and then joining the resulting points by means of straight lines. A frequency polygon can also be obtained by joining the mid points of the tops of rectangles in the histogram.To construct a frequency polygon, we mark the class marks along the X-axis and class frequencies along the Y-axis points are obtained by plotting the class frequencies against their corresponding class mark. The points so formed are joined by means of straight lines. The ends of the graphs so drawn do not meet the X-axis. We know that a polygon is a many sided closed figure we therefore add extra classes at both of the frequency distribution with zero frequencies. By doing so the polygon forms a closed figure.

Frequency Curve

If the frequency polygon is smoothed out, the resulting graph is called a frequency curve.

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Q. No. 2: Define the Frequency Distribution and write the steps involved in the construction of frequency distribution.

FREQUENCY DISTRIBUTION

A tabular arrangement of data by classes together with the corresponding class frequencies is called a frequency distribution or frequency table.

A frequency-distribution of heights (recorded to the nearest inch) of 100 male students at ABC college.

Heights of 100 male students at ABC collage

Height(inch) Number of students60-----6263-----6566-----6869-----7172-----74

51743269

Total 100

The first class, consist of heights from 60---62 and is indicated 5 students have heights in the range, here class frequency is 5. Data organized in the above table are often called group data. Although the grouping of data destroy much of the original detail but important advantage is that it gives clear overall picture of the mass data in tabular form.

Class Limits

Class or a group is described by two numbers. These numbers are called class limits, the smaller number is called lower class limit and the greater is upper class limit. In table 3.5.1 in height column first group 60—62, here 60 is lower and 62 is upper class limit.

Class Boundries

The actual or precise numbers which separate one class limit from another are called class boundaries.

The class boundaries are obtained by adding the upper limit and lower limit and dividing by 2.

Example: If heights are recorded to the nearest inch the class limit 60---62 theoretically includes all measurement from 59.5 to 62.5 inches. Here 59.5----62.5 is the class boundary.

Class Mark

It is the mid point of the class limit and is obtained by adding the upper and lower class limit or class boundary by 2

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Thus the class mark of the group 60----62 is 60+62 / 2 = 61

Class Width Or Interval

It is usually denoted by h or c and is equal to the difference between the class boundaries h or c is the common width if all the class intervals are of equal size

Height (Inches)

Class limits

Number of students

F

Mid pointX

Class boundaries

60-----6263-----6566-----6869-----7172-----74

51743269

6164677073

59.5-----62.562.5-----65.565.5-----68.568.5-----71.571.5-----74.5

100

Example:

Make a grouped frequency distribution from the following data relating to the weight recorded to the nearest grams of 60 apples picked out at random from a consignment.106 107 76 82 109 107 115 93 187 95 123 125 111 92 86 70 126 68 130 129 139 119 115 128 100 186 84 99 113 204 111 141 136 123 90 115 98 110 78 185 162 178 140 152 173 146 158 194 148 90 107 181 131 75 184 104 110 80 118 82 By scanning the data we find that the largest weight is 204 grams and the smallest weight is 68 grams so that the range is 204 – 68 = 136 grams suppose we decide to take 7 classes of equal size then size or width of the equal class interval would be 136/7 = 19.47 but we take H equal to 20, the next integral value higher than 19.47 to facilitate the numerical work. Let us decide to locate the lower limit of the lowest class at 65. with this choice. The class limits will be 65---84. 85---104, 105---124, …., the class boundaries become 64.5- 84.5, 84.5-104.5, 104.5-124.5, …, and the class marks are 74.5,94.5,114.5,…, the grouped frequency distribution is then constructed as follows:

Weight Entries Frequency 65---84 85---104105---124

125---144145---164165---184185---204

76,82,70,68,84,78,75,80,8293,95,92,86,100,99,90,98,90,104106,107,109,107,115,123,111,119,115,113,111,123,115,110,107,110,118125,126,130,129,139,128,141,136,140,131162,152,146,158,148178,173,181,184187,186,204,185,194

91017

10545

Total 60

This table is some times known as an entry table. The values against each class may be arrange in an array.

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BY USING A TALLY COLUMN Frequency distribution of weights of 60 apples

ClassesWeight

Class boundaries

Mid. Points Tally Frequency

65---8485---104105---124125---144145---164165---184185---204

64.5---84.584.5---104.5104.5---124.5124.5---144.5144.5---164.5164.5---184.5184.5---204.5

74.594.5114.5134.5154.5174.5194.5

//// llll//// //////// //// ll//// ////////llll////

9101710545

Total 60

Q. No. 3: Discuss the different scales of measurement

Measurement Scales

By measurement, we usually mean the assigning of numbers to observations or objects and scaling is a process of measuring. The four scales of measurement are briefly mentioned below.

Nominal Scale

The classification or grouping of the observations into mutually exclusive qualitative categories or classes is said to constitute a nominal scale. For example: students are classified as male and female. Number 1 and 2 may also be used to identify these two categories. Similarly, rainfall may be classified as heavy, moderate and light. We may use number 1, 2 and three to denote the three classes of rainfall. The numbers when they are used only to identify the categories of the given scale carry no numerical significance and there is no particular order for the grouping.

Ordinal or Ranking Scale

It includes the characteristic of a nominal scale and in addition has the property of ordering or ranking of measurements. For example, the performance of students (or players) is rated as excellent, good, fair or poor, etc. number 1, 2, 3, 4, etc. are also used to indicate ranks. The only relation that holds between any pair of categories is that of greater than (or more preferred)

Interval Scale

A measurement scale possessing a constant interval size (distance) but not a true zero point, is called an interval scale. Temperature measured on either the Celsius or the Fahrenheit scale is an outstanding example of interval scale because the same difference exists between 20°C (68°F) and twice as hot as a temperature of 20 degree, i.e. the ratio 40/20 has no meaning. The arithmetic operation of addition, subtraction, etc. are meaningful.

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Ratio Scale

It is a special kind of an interval scale of measurement has a true zero point as its origin. The ratio scale is used to measure weight, volume, length, distance, money, etc. the key to differentiating interval and ratio scale is that the zero point is meaningful for ratio scale.

Example of Measurement Scales

Nominal-level data Ordinal-level data Interval-level data Ratio-levelGender (Male, Female)Eye colourReligion

Specialization

Nationality

Grades(A, B, C, D, f)Position (Ist,2nd,3rd,etc.)Ranking of cricket player.Rating(poor, good, excellent)Socio-economic status(poor, middle class, rich)

TemperatureIQ scoreSAT score

AgeWeightHeightTime

SalaryDistance

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