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Presentation On Analytical Characteristics of Bangladesh By Division Submitted to M. Amir Hossain, Ph.D. Professor, Applied Statistics D.U. East West University, Bangladesh.  H.M. Faisal Ahmed2010-2-91-021 Submitted By Group C INTRODUCTION  Data Presentation  WehavecollecteddemographicdatafromBBS (BangladeshBureauofStatistics)website www.bbs.gov.bd/Home.aspx.Wedecidedtocollecttwo types of data (Qualitative & Quantitative).For Qualitative datawehaveconsideredthedataabouttheLandArea, andnumberofMaleandFemaleinadivisionandfor quantitative data we have considered the data about age. WehaveappliedthedataindifferenttypesofData Presentation techniques. TECHNIQUES USED  Bar Chart  Histogram  Frequency Polygon  Cumulative Frequency Curve FACT TABLE  The Bar chart and Histogram are based on the following fact table:  Based on Enumerated population in 2011 DIVISIONAREAMALEFEMALE BARISAL 13,645 4,006,000 4,140,000 CHITTAGONG 33,771 13,763,000 14,361,000 DHAKA 30,989 23,814,000 22,915,000 RAJSHAHI 34,495 9,183,000 9,146,000 KHULNA 22,285 7,782,0007,781,000 SYLHET 12,596 4,882,000 4,925,000 BAR CHART  A bar chart or bar graph is a way of showing information by the lengths of a set of bars. The bars are drawn horizontally orvertically.Ifthebarsaredrawnvertically,thenthegraph canbecalledacolumngraphorablockgraph.Achart whichdisplaysasetoffrequenciesusingbarsofequal width whose heights are proportional to the frequencies.  Inourpresentationtheheightofthebarsrepresentsthe numberofdifferentindividuals,theXaxisrepresents different division and Y axis the number of individuals. BAR CHART (CONTINUED) Chart 01: Bar Chart of Male and Female per Division BAR CHART (CONTINUED) 14 34 31 34 22 13 0 5 10 15 20 25 30 35 40 Thousands B a r i s a l C h i t a g o n g D h a k a R a j s h a h i K h u l n a S y l h e t Land Area (Square Killometer) Chart 2: Bar Chart of Land Area per Division HISTOGRAM  A graphical representation, similar to a bar chart in structure, thatorganizesagroupofdatapointsintouser-specified ranges.Thehistogramcondensesadataseriesintoan easilyinterpretedvisualbytakingmanydatapointsand groupingthemintologicalrangesorbins.Instatistics,a histogramisagraphicaldisplayoftabulatedfrequencies, shownasbars.Itshowswhatproportionofcasesfallinto each of several categories: it is a form of data binning. The categories are usually specified as non-overlapping intervals ofsomevariable.Thecategories(bars)mustbeadjacent. The intervals are generally of the same size.  Histogramsareusedtoplotdensityofdata,andoftenfor densityestimation:estimatingtheprobabilitydensity function of the underlying variable. HISTOGRAM (CONTINUED) Chart 04: Histogram of Male & Female per Division HISTOGRAM (CONTINUED) 0 5000 10000 15000 20000 25000 30000 35000 40000 Chittagong Division Dhaka Division Khulna Division Rajshai Division Sylhet Division Chart 05: Histogram of Land Area per Division FREQUENCY POLYGON  A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval (Class Mark). The points are connected so that together with the X-axis they form a polygon.  In our presentation Class Marks (Class Mid Points) are plotted through X axis and Number of individuals in that class are plotted through Y axis. FREQUENCY POLYGON (CONTINUED)  Frequency Distribution Table (With class Mark) ClassClass MarkFrequency 40-44427133824 45-49475152206 50-54524322404 55-59572774265 60-64622662799 64-69671758685 70-74721461443 ClassClass MarkFrequency 00-04214465810 05-09716534124 10-141215704322 15-191712186950 20-242210688351 25-29279858549 30-34329363144 35-39378198944 FREQUENCY POLYGON (CONTINUED) - 2 4 6 8 10 12 14 16 18 - 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Age P o p u l a t i o n N u m b e r Millions Chart 06: Frequency Polygon of peoples age Information of Bangladesh CUMULATIVE FREQUENCY CURVE  Also known as an ogive, this is a curve drawn by plotting the value of the first class on a graph. The next plot is the sum of the first and second values, the third plot is the sum of the first, second, and third values, and so on. The total of a frequency and all frequencies below it in a frequency distribution.  In our presentation cumulative frequency of age groups is plotted through Y axis and Class Frequency through Class Mark is plotted through X axis. CUMULATIVE FREQUENCY CURVE (CONT.) ClassClass MarkFrequency Cumulative Frequency 00-0421446581014465810 05-0971653412430999935 10-14121570432246704257 15-19171218695058891207 20-24221068835169579559 25-2927985854979438108 30-3432936314488801253 35-3937819894497000197 CUMULATIVE FREQUENCY CURVE (CONT.) ClassClass MarkFrequency Cumulative Frequency 40-44427133824104134021 45-49475152206109286228 50-54524322404113608632 55-59572774265116382897 60-64622662799119045696 64-69671758685120804382 70-74721461443122265825 CUMULATIVE FREQUENCY CURVE (CONT.) 0 20 40 60 80 100 120 140 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Age P o p u l a t i o n N u m b e r s Millions Chart 07: Cumulative Frequency Curve of Age Information of Bangladesh COMMENT  The Assignment was done within short time that‟s why there might be some errors in our analysis but still the data will be able to visualize the actual picture. MEASURES OF DISPERSION Thedescriptivestatisticsthatmeasurethe qualityofscatterarecalledmeasuresof dispersion.Measuresofdispersiongivea morecompletepictureofthedataset.It deals with spread of data. A small value of themeasureofdispersionindicatesthat data are clustered closely. A large value of dispersion indicates the estimate of central tendency is not reliable. TYPES OF MEASURES OF DISPERSION There are many type of measurement of dispersion, herewe discuss as below- Absolute Measures of Dispersion: These measures give us an idea about the amount of dispersion in a set of observations.Theygivetheanswersinthesameunitsastheunitsofthe original observations. When the observations are in kilograms, the absolute measure is also in kilograms. If we have two sets of observations, we cannot alwaysusetheabsolutemeasurestocomparetheirdispersion.Weshall explain later as to when the absolute measures can be used for comparison ofdispersionintwoormorethantwosetsofdata.Theabsolutemeasures which are commonly used are: 1. Range 2. Mean Deviation 3. Variance 4. Standard Deviation Relative Measure of Dispersion: These measures are calculated for the comparison of dispersion in two or more than two sets of observations. These measures are free of the units in which the original data is measured. If the original data is in dollar or kilometers, we do not use these units with relative measure of dispersion. These measures are a sort of ratio and are called coefficients. Each absolute measure of dispersion can be converted into its relative measure. Hear we only discuses: 1. Coefficient of Variance TYPES OF MEASURES OF DISPERSION RANGE For ungroup data: The simplest measure of dispersion is the range.Therangeiscalculatedbysimplytakingthe differencebetweenthemaximumandminimumvaluesin the data set. Range=Highest Value-Lowest Value Forgroupdata:Iftherearegroupdatathantherangeis calculatedbytakingthedifferencebetweentheupperlimit of the highest class and the lower limit of the lowest class. Range= upper limit of the highest class- lower limit of the lowest class. MEAN DEVIATION Themeandeviationisthefirstmeasure ofdispersionthatwewillusethatactually uses each data value in its computation. It is the mean of the distances between each value and the mean. It gives us an idea of howspreadoutfromthecenterthesetof values is. For ungroup data: For group data: MD X X n = ÷ E f | X X | f MD E ÷ E = I I VARIANCE Varianceisamathematicalexpressionof theaveragesquareddeviationsfromthe mean.Wecansaidalso,thearithmetic meanofthesquaresofthedeviationsof allvaluesinasetofnumbersfromtheir arithmetic mean.  Population Variance: _  Sample Variance: o µ 2 2 = ÷ E( ) X N 1 ) ( 2 2 ÷ ÷ E = n X X S VARIANCE Working formula for population variance is: Working formula for sample variance is: 2 2 2 ) ( N X N X E ÷ E = o 1 ) ( S 2 2 2 ÷ E ÷ E = n n X X RELATIVE DISPERSION  Theusualmeasureofdispersioncannotbe usedtocomparethedispersioniftheunits aredifferent,eventheunitaresamebutthe means are different.  It reports variation relative to the mean.  Itisusefulforcomparingdistributionswith different units. Hear we only discuses: 1. Coefficient of Variation COEFFICIENT OF VARIANCE TheCVistheratioofthestandard deviationtothearithmeticmean, expressedasapercentage.Wecanalso said, to compare the variations (dispersion) of two different series, relative measures of standarddeviationmustbecalculated. This is known as co-efficient of variation. The formula of CV is given bellow: 100 × = X s CV Class IntervalFrequencyX/Midpointxf-- ---- f 00-04 05-09 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 14.46 16.53 15.70 12.18 10.68 9.85 9.36 8.19 7.13 5.15 4.32 2.77 2.66 1.75 1.46 2 7 12 17 22 27 32 37 42 47 52 57 62 67 72 28.92 115.78 188.4 207.06 234.96 265.95 299.52 303.03 299.46 242.05 224.64 157.89 164.92 117.25 105.12 -22.18 -17.18 -12.18 -7.18 -2.18 2.82 7.82 12.82 17.82 22.82 27.82 32.82 37.82 42.82 47.82 22.18 17.18 12.18 7.18 2.18 2.82 7.82 12.82 17.82 22.82 27.82 32.82 37.82 42.82 47.82 320.72 283.98 191.22 87.45 23.68 27.77 73.19 104.99 127.05 117.52 120.18 90.91 100.60 74.93 69.81 491.95 295.15 148.35 51.55 4.75 7.95 61.15 164.35 317.55 520.75 773.95 1077.15 1430.35 1833.55 2286.75 7113.59 4878.82 2329.09 627.87 50.73 78.30 572.364 1346.02 2264.13 2681.86 3343.46 2983.70 3804.73 3208.71 3338.65 122.192954.95181438700.32 X X ÷ | | X X ÷ | | X X ÷ ( ) 2 X X ÷ ( ) 2 X X f ÷ Range= 74-0 = 74 _ X= 2954.95/122.19= 24.18 _ Mean Deviation= = 1814/122.19=14.8457 f | | f E ÷ E X X EXAMPLE Determination of the year 2011: Figure in “Mil” Variance,=38700.32/122.19= 316.72 Standard Deviation= = 17.7966 Coefficient of Variance (CV)= = (17.7966/24)X100 = 74.15% ( ) f X X S E ÷ E = 2 | | . | \ | ÷ ÷ E = = 1 ) ( 2 2 n X X S S 100 × = X s CV | . | \ | = 122.19 38700.32 CORRELATION Helps to take decision and identifying the nature of business and economic decisions Helpful in identifying the nature of relationship among many business and economic variables One variable depends on another and can be determined by it The Coefficient of Correlation (r) is a measure of the strength of the relationship between two variables. It requires interval or ratio-scaled data (variables). It can range from -1.00 to 1.00. Values of -1.00 or 1.00 indicate perfect and strong correlation. Values close to 0.0 indicate no linear correlation. Negative values indicate an inverse relationship and positive values indicate a direct relationship DATA TABLE XY X- X^Y-Y^(X-X^)(Y-Y^)(X-X^) 2 (Y-Y^) 2 341 -2-14284196 7 76 221424441 6 56 11111 5 78 02300529 2 43 -3-12369144 1 34 -4-218416441 X^ = 5Y^ = 55 ¿(X-X^)(Y-Y^) =191 ¿X-X^) 2 = 34¿ (Y-Y^) 2 = 1752 VALUEOF‘R’ r = 0.78 Comment:As, the value or „r‟ is positive , so the variables have stronger relation between them. REGRESSION Aregressionisastatisticalanalysisassessingtheassociation betweentwovariables.Itisusedtofindtherelationship between two variables. General form of linear regression model Y = a + bX + e Where, Y : dependent variable a : intercept term b : slope of the line X : independent variable e : error term Want to estimate a and b such that ∑e 2 is minimum REGRESSION ANALYSIS XY X-ẊY- Ȳ(X- Ẋ)(Y- Ȳ)(X- Ẋ) 2 341 -2-14284 7 76221424 6 561111 5 78 02300 2 43 -3-12369 1 34 -4-218416 Ẋ= 5Ȳ= 55 ¿(X- Ẋ)(Y- Ȳ) =191 ¿(X- Ẋ)2 = 34 REGRESSION ANALYSIS So, Here after putting the value, = 191/34 = 5.6 a= 55 - 5.6(5) =27  Form the linear regression model, Y = 27 + 5.6X Here regression coefficient is 5.6 that means if we change 1 unit of independent variable, dependent variable will change 5.6. THANK YOU
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