Graphical & Diagrammatic representation of Data

Graphical Representation of Data Dr.R.Jayashree Asst.Prof (AGB) Veterinary College, Hebbal

Graph is a visual form of presentation of quantitative data.

Graphic methods enable to present quantitative data in a simple, clear and effective manner in comparison to numerical facts.

Dr. R Jayashree, Asst. Prof(AGB) College, Hebbal, Bangalore

Veterinary

Types of Graphs 1.

2.

3.

4.

Histogram Frequency Polygon Frequency curves Cummulative Frequency curves or “ogives” 5. Lorenz curve

Dr. R Jayashree, Asst. Prof(AGB) Veterinary College, Hebbal, Bangalore

Guiding principles for construction of Graph Y

X’

O

X

Y’

Horizontal line X’OX is called abscissa Vertical line YOY’ is called ordinate.

In practice only the first quadrant is used unless negative R Jayashree, Asst. Prof(AGB) magnitudes are to beDr.displayed.

Bar Graph A bar graph is a graphical representation of frequency distributions of ungrouped data.

It is • A pictorial representation of the numerical data by a number of bars (rectangles) of uniform width erected vertically (or horizontally) with equal spacing between them.

Dr. R Jayashree, Asst. Prof(AGB)

The number of trees planted by an agency in different years is given below : Years 1997 1998 1999 2000 2001 2002 Total Number of trees planted 400 450 700 750 900 1500 4700

Dr. R Jayashree, Asst. Prof(AGB)

Simple Bar Graph

Dr. R Jayashree, Asst. Prof(AGB)

Divided Bar Graph

Dr. R Jayashree, Asst. Prof(AGB)

Histogram A histogram is a graphical representation of a continuous frequency distribution i.e. grouped frequency distributions.

For each class, a rectangle is drawn with base as width of the class and height as the class frequency.

Dr. R Jayashree, Asst. Prof(AGB)

Histogram

The class-intervals are taken along the horizontal axis and the respective class frequencies on the vertical axis using suitable scales on each axis.

Dr. R Jayashree, Asst. Prof(AGB)

10 0

Frequency

Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1

20

Histogram

0

10 20 30 40 50 60 70 80 Years

Dr. R Jayashree, Asst. Prof(AGB)

10 0

Frequency

Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1

20

Histogram Construction

0

10 20 30 40 50 60 70 80 Years

Dr. R Jayashree, Asst. Prof(AGB)

Histogram with unequal classes • As in equal classes the histograms are drawn except for the heights of the bars.

• The height is adjusted so that the area of the rectangle is equal to the frequency of corresponding class.

• This adjustment is done by taking the height of the bar proportional to the frequency density of each class.

Dr. R Jayashree, Asst. Prof(AGB)

Example of Unequal Class Class interval

No of chickens that died

10-12

23

12-24

24

24-30

55

30-42

34

42-48

12

48-50

10 Dr. R Jayashree, Asst. Prof(AGB)

Frequency density Frequency density=

Frequency of the class adjustment factor

Width of the Class Adjustment factor of class= Width of the lowest class interval

This adjustment gives the bars with an indication that the areas are equal to the frequencies of the corresponding classes Dr. R Jayashree, Asst. Prof(AGB)

2 4 6 8 10 12 14 16 18 20 22 24 10

Class interval

No of chickens that died

Adjustment factor

Frequency density

10-12

23

2/2=1

23/1=23

12-24

24

12/2=6

24/6=4

24-30

55

6/2=3

55/3=18.33

30-42

34

12/2=6

34/6=5.67

42-48

12

6/2=3

12/3=4

48-50

10

2/2=1

10/1=10

15

Dr. Asst. Prof(AGB) 20R Jayashree, 25 30 40 45

50

55

Frequency polygon • In a frequency distribution, the mid-value of each class is obtained.

• Then on the graph paper, the frequency is plotted against the corresponding midvalue.

• These points are joined by straight lines.

These straight lines may be extended in both directions to meet the X - axis to form a polygon Dr. R Jayashree, Asst. Prof(AGB)

R Jayashree, Asst. in Prof(AGB) A frequency polygonDr. has been shown dotted lines.

Frequency Polygon

Dr. R Jayashree, Asst. Prof(AGB)

10 0

Frequency

Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1

20

Frequency Polygon

0

10 20 30 40 50 60 70 80 Years

Dr. R Jayashree, Asst. Prof(AGB)

Cummulative Frequency curve • It is desirable to determine the number of observations that fall above or below a certain value rather than within the class interval.

• The regular frequency distribution may be converted to cumulative frequency distribution and the graph is called as “Ogive” Dr. R Jayashree, Asst. Prof(AGB)

Methods of constructing ogives 1. Less than method.2. More than method.

Class Frequency Interval

Less than ogive

More than ogive

40-45

3

3

32

46-51

9

12

29

52-57

12

24

20

58-63

5

29

8

64-69

1

30

3

70-75

2

32

2

Dr. R Jayashree, Asst. Prof(AGB)

Class Interval

Frequency

Less than ogive

More than ogive

40-45

3

3

32

46-51

9

12

29

52-57

12

24

20

58-63

5

29

8

64-69

1

30

3

70-75

2

32

2

35 30 25 20

Ser i es1 Ser i es2

15 10 5 0 40-45

46-51

52-57

58-63

64-69

70-75

Dr. R Jayashree, Asst. Prof(AGB)

Lorenz Curve

This is Modification of Ogive curve. It is drawn when the variables and the cummulative frequencies are expressed as percentages.

Use- In picturising the dispersion of wealth, sales and profits etc.

Dr. R Jayashree, Asst. Prof(AGB)

District

Surthi

Murrah

Bangalor e(U)

3143

370

25000 20000

2045

2995

Bidar

1539

697

Bijapur

1069

642

Chickma galur

2853

324

Chitradur ga

4965

476

D.Kanna da

3031

549

Dharwad

8411

635

5000 0

Dr. R Jayashree, Asst. Prof(AGB)

Bi ja pu r ck m ag al ur Ch itr ad ur ga D. Ka nn ad a Dh ar w ad

Bellary

Series1

10000

Ch i

5000

da r

15835

Series2

Bi

Belgaum

15000

Be lla ry

785

lo re (U Ba ) ng al or e速 Be lg au m

4717

Ba ng a

Bangalor e速

Area Graph

Symmetrical Graph

The frequencies are more or less symmetrically distributed, around a mean class

Dr. R Jayashree, Asst. Prof(AGB)

Skewed Distribution

The frequencies are more or less asymmetrically distributed, containing values that are substantially smaller on one of the sides, relative to the other: Dr. R Jayashree, Asst. Prof(AGB)

Distributions with long Tails

The frequencies are distributed so that there are a large number of classes at either end, with small frequencies compared to the central classes

Dr. R Jayashree, Asst. Prof(AGB)

Distributions with various "peaks" or modes

The distribution of frequencies has two or more "peaks", which we call modes, suggesting that the data comprise various distinct groups: Dr. R Jayashree, Asst. Prof(AGB)

Diagrammatic Representation of Data

Diagrammatic

Presentation of data Tabular

Line Diagram

Bar Diagram

Pie Diagram

Area Diagram

Simple Bar Diagram

Sub divided Bar Diagram

Percentage Bar Diagram

Pictogram

Multiple Bar Diagram

Dr. R Jayashree, Asst. Prof(AGB)

Presentation of Statistical data 1. Tabular Presentation

2. Diagrammatic or Graphic presentation.

Dr. R Jayashree, Asst. Prof(AGB)

Advantages of Diagrammatic Representation

• • • •

Give a birds eye view of numerical set of data.

More appealing.

Highlight the salient features of the data.

Self explanatory Dr. R Jayashree, Asst. Prof(AGB)

Limitations • Cannot be analyzed further • Only useful to common man and not much to an expert.

• Primarily serve in comparative study and functional relationship between the variables under study.

Dr. R Jayashree, Asst. Prof(AGB)

Types of Diagrams 1.

2.

3.

4.

5.

Line Diagrams Bar Diagrams Pie diagrams Area diagrams Pictograms

Dr. R Jayashree, Asst. Prof(AGB)

Moisture Protein Fat Ash Cholestrol

Line Diagram • Simplest of all diagrams.

• Consists of drawing vertical lines which mention the variable.

• X axis – Variable values are presented • Y axis – corresponding frequencies are presented.

Dr. R Jayashree, Asst. Prof(AGB)

Line Diagram

Hundreds

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 4500 4000 3500 3000 2500 2000 1500 1000 500 0

Dr. R Jayashree, Asst. Prof(AGB)

Series1

Bar Diagram • This consists of a group of equidistant rectangles or bars one for each group or category of data in which the values or magnitudes are represented by the length or height of the rectangles. • All the bars should be uniform and should be constructed on the same base line for a single study.

Dr. R Jayashree, Asst. Prof(AGB)

Method of getting to school

Number of students

School bus

58

Car

7

Walk

35

Cycle

12

Public transit

18

Other

0

Dr. R Jayashree, Asst. Prof(AGB)

Types of Bar Diagram 1.

2.

3.

4.

Simple bar diagram Sub-divided or component bar diagram Percentage bar diagram Multiple bar diagram

Dr. R Jayashree, Asst. Prof(AGB)

Simple Bar Diagram • In this the magnitude of the observation of the observations are represented by the heights or lengths of the bar. • Limitation: It allows studying only one character only at a time.

Dr. R Jayashree, Asst. Prof(AGB)

Sub divided bar Diagram or Component bar Diagram • It is used to subdivide the magnitude of the given variable into various parts or sub-classes or components. • It useful for presenting several items or characteristics of a variable or a category simultaneously.

Dr. R Jayashree, Asst. Prof(AGB)

Crossbred cattle in selected districts 120000 100000 80000 60000 40000 20000 0 Bangalore(U)

Series2 Series1 Dharw ad

Tum kur

Districts

Composition of Chicken & Beef

150 100

60

50

63

Beef Chicken

0 Moisture

16.1 19

22 11

0.9 1

Fat

Dr. R Jayashree, Asst. Prof(AGB)

1 6 Cholestrol

Percentage bar diagram • Subdivide bar diagram presented graphically on percentage basis gives percentage bar diagram. • All the bars will be of same height with various segments of the bar representing the different components. • Used for diagrammatic portrayal of the relative changes in the data.

Dr. R Jayashree, Asst. Prof(AGB)

100%

Tumkur

80%

Shimoga Mandya

60%

Dharwad

40%

D.Kannada Bidar

20%

Bangalore(U)

0% 1

2

Composition of meat of various animals 100% 80%

Rabbit

60%

Lamb Pork

40%

Beef

20%

Chicken

0% Moisture

Fat

Cholestrol

Dr. R Jayashree, Asst. Prof(AGB)

Multiple bar diagram • This is used if two or more sets of interrelated phenomenon or variables are to be represented.

• It is similar to drawing of simple bar diagram but in this case a set of adjacent bars one for each variable is drawn.

• Proper and equal spacing is given for the sets of bars.

Dr. R Jayashree, Asst. Prof(AGB)

Major nutrients in meat of different Animals 100 50 Moisture 0

Chic Beef Pork Lam Rab

Moisture 63

60

56

70

Protein

19 16.1 11.9 15

20

Fat

11

6

22

42 45

27

Dr. R Jayashree, Asst. Prof(AGB)

Protein Fat

Pie diagram/Angular diagram • This is circular diagram • Used to represent the total magnitude of various components.

• The circle is divided into various sections or segments representing certain proportions or percentage of various component parts to the total.

Dr. R Jayashree, Asst. Prof(AGB)

Pie Diagram • The degrees represented by the various components of a given magnitude or quantity in a pie/circle can be obtained as follows • Degree of Component value Χ 360 any component=

Total value

Dr. R Jayashree, Asst. Prof(AGB)

Dr. R Jayashree, Asst. Prof(AGB)

Pictogram • Presenting Statistical data through pictures.

Dr. R Jayashree, Asst. Prof(AGB)