Presentation On Analytical Characteristics of Bangladesh

By Division

Submitted toM. Amir Hossain, Ph.D.Professor, Applied StatisticsD.U.East West University, Bangladesh.

H.M. Faisal Ahmed 2010-2-91-021

Submitted By

Group C

Data Presentation We have collected demographic data from BBS

(Bangladesh Bureau of Statistics) website www.bbs.gov.bd/Home.aspx. We decided to collect two types of data (Qualitative & Quantitative). For Qualitative data we have considered the data about the Land Area, and number of Male and Female in a division and for quantitative data we have considered the data about age. We have applied the data in different types of Data Presentation techniques.

Bar Chart Histogram Frequency Polygon Cumulative Frequency Curve

The Bar chart and Histogram are based on the following fact table:

Based on Enumerated population in 2011

DIVISION AREA MALE FEMALE

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 7,782,000 7,781,000

SYLHET 12,596 4,882,000 4,925,000

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 or vertically. If the bars are drawn vertically, then the graph can be called a column graph or a block graph. A chart which displays a set of frequencies using bars of equal width whose heights are proportional to the frequencies.

In our presentation the height of the bars represents the number of different individuals, the X axis represents different division and Y axis the number of individuals.

Chart 01: Bar Chart of Male and Female per Division

14

34

31

34

22

13

0

5

10

15

20

25

30

35

40

Thousands

Land Area (SquareKillometer)

Chart 2: Bar Chart of Land Area per Division

A graphical representation, similar to a bar chart in structure, that organizes a group of data points into user-specified ranges. The histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins. In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories: it is a form of data binning. The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent. The intervals are generally of the same size.

Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable.

Chart 04: Histogram of Male & Female per Division

Chart 05: Histogram of Land Area per Division

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 Distribution Table (With class Mark)

Class Class Mark Frequency

40-44 42 7133824

45-49 47 5152206

50-54 52 4322404

55-59 57 2774265

60-64 62 2662799

64-69 67 1758685

70-74 72 1461443

Class Class Mark Frequency

00-04 2 14465810

05-09 7 16534124

10-14 12 15704322

15-19 17 12186950

20-24 22 10688351

25-29 27 9858549

30-34 32 9363144

35-39 37 8198944

-2

46

810

1214

1618

- 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Age

Po

pu

lati

on

Nu

mb

er

Millions

Chart 06: Frequency Polygon of peoples age Information of Bangladesh

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.

Class Class Mark FrequencyCumulative

Frequency

00-04 2 14465810 14465810

05-09 7 16534124 30999935

10-14 12 15704322 46704257

15-19 17 12186950 58891207

20-24 22 10688351 69579559

25-29 27 9858549 79438108

30-34 32 9363144 88801253

35-39 37 8198944 97000197

Class Class Mark FrequencyCumulative

Frequency

40-44 42 7133824 104134021

45-49 47 5152206 109286228

50-54 52 4322404 113608632

55-59 57 2774265 116382897

60-64 62 2662799 119045696

64-69 67 1758685 120804382

70-74 72 1461443 122265825

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

Po

pu

lati

on

Nu

mb

ers

Millions

Chart 07: Cumulative Frequency Curve of Age Information of Bangladesh

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 DISPERSIONMEASURES OF DISPERSION

The descriptive statistics that measure the quality of scatter are called measures of dispersion. Measures of dispersion give a more complete picture of the data set. It deals with spread of data. A small value of the measure of dispersion indicates that data are clustered closely. A large value of dispersion indicates the estimate of central tendency is not reliable.

TYPES OF MEASURES OF TYPES OF MEASURES OF DISPERSIONDISPERSION

There are many type of measurement of dispersion, here we discuss as below-

 Absolute Measures of Dispersion:

These measures give us an idea about the amount of dispersion in a set of observations. They give the answers in the same units as the units of the original observations. When the observations are in kilograms, the absolute measure is also in kilograms. If we have two sets of observations, we cannot always use the absolute measures to compare their dispersion. We shall explain later as to when the absolute measures can be used for comparison of dispersion in two or more than two sets of data. The absolute measures which are commonly used are:

1. Range2. Mean Deviation3. Variance4. 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

For ungroup data: The simplest measure of dispersion is the range. The range is calculated by simply taking the difference between the maximum and minimum values in the data set.

Range=Highest Value-Lowest Value

For group data: If there are group data than the range is calculated by taking the difference between the upper limit 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 DEVIATIONMEAN DEVIATION

The mean deviation is the first measure of dispersion that we will use that actually 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 how spread out from the center the set of values is.

For ungroup data:

For group data:

MDX X

n

f

|XX|f MD

I I

VARIANCEVARIANCE

Variance is a mathematical expression of the average squared deviations from the mean. We can said also, the arithmetic mean of the squares of the deviations of all values in a set of numbers from their arithmetic mean.

Population Variance:

_ Sample Variance:

2

2

( )X

N

1

)( 22

n

XXS

Working formula for population variance is:

Working formula for sample variance is:

22

2 )(N

X

N

X

1

)(

S

22

2

nnX

X

The usual measure of dispersion cannot be used to compare the dispersion if the units are different, even the unit are same but the means are different.

It reports variation relative to the mean. It is useful for comparing distributions with

different units.

Hear we only discuses:

1. Coefficient of Variation

The CV is the ratio of the standard deviation to the arithmetic mean, expressed as a percentage. We can also said, to compare the variations (dispersion) of two different series, relative measures of standard deviation must be calculated. This is known as co-efficient of variation.

The formula of CV is given bellow:

100X

sCV

Class Interval Frequency X/Midpoint xf -- -- --f

00-0405-0910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-74

14.4616.5315.7012.1810.689.859.368.197.135.154.322.772.661.751.46

27

12172227323742475257626772

28.92115.78188.4207.06234.96265.95299.52303.03299.46242.05224.64157.89164.92117.25105.12

-22.18-17.18-12.18-7.18-2.182.827.82

12.8217.8222.8227.8232.8237.8242.8247.82

22.1817.1812.187.182.182.827.82

12.8217.8222.8227.8232.8237.8242.8247.82

320.72283.98191.2287.4523.6827.7773.19

104.99127.05117.52120.1890.91

100.6074.9369.81

491.95295.15148.3551.554.757.95

61.15164.35317.55520.75773.95

1077.151430.351833.552286.75

7113.594878.822329.09627.8750.7378.30

572.3641346.022264.132681.863343.462983.703804.733208.713338.65

122.19 2954.95 1814 38700.32

XX || XX || XX 2XX 2XXf

Range= 74-0 = 74_ X= 2954.95/122.19= 24.18

_Mean Deviation= = 1814/122.19=14.8457 f

||f

XX

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

XXS

2

1

)( 22

n

XXSS

100X

sCV

122.19

38700.32

Helps to take decision and identifying the nature of business and economic decisionsHelpful in identifying the nature of relationship among many business and economic variablesOne 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

X Y

X- X^ Y-Y^ (X-X^)(Y-Y^) (X-X^)2 (Y-Y^)2

3 41

-2 -14 28 4 196

7 762 21 42 4 441

6 561 1 1 1 1

5 78

0 23 0 0 529

2 43

-3 -12 36 9 144

1 34

-4 -21 84 16 441

X^ = 5 Y^ = 55

(X-X^)(Y-Y^)=191

X-X^)2 = 34 (Y-Y^)2

= 1752

r = 0.78

Comment: As, the value or ‘r’ is positive , so the variables have stronger relation between them.

A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.General form of linear regression model Y = a + bX + eWhere,

Y : dependent variable a : intercept term b : slope of the line

X : independent variable e : error termWant to estimate a and b such that ∑e2 is minimum

X YX- Ẋ Y- Ȳ (X- Ẋ)(Y- Ȳ) (X- Ẋ)2

3 41 -2 -14 28 4

7 76 2 21 42 4

6 56 1 1 1 1

5 78 0 23 0 0

2 43 -3 -12 36 9

1 34-4 -21 84 16

Ẋ= 5 Ȳ= 55

(X- Ẋ)(Y- Ȳ)

=191

(X- Ẋ)2 = 34

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 YOUTHANK YOU