Graphical representation of data

Classification according to class interval Dept. of AGB Veterinary College Hebbal

Frequency table Upper boundary

Lower limit

Lower boundary Class Interval

Class width

Class 30-34 34-38 38-42 42-46 46-50 Total

Frequency 5 15 5 3 2 30 Upper limit

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

Choice of the class interval Exclusive 0-10 10-20 20-30

Excluding the upper limit

Inclusive 0 to 10 10 to 20 20 to 30

Mid value 5 10 15

Including the upper limit Dr. R Jayashree, Asst. Prof(AGB) Veterinary College, Hebbal, Bangalore

Lower + Upper Divided by 2

Choice of the class interval (Contd.)

Open end class

Unequal class

Class limit exactly defined

Less than 20 20-30 30-40 More than 40

0-10 10-12 12-30 30-50

0-9.9 10-19.9 20-29-9 30-30.9

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

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) Veterinary College, Hebbal, Bangalore

Types of Graphs 1.

2.

3.

4.

5.

Histogram Frequency Polygon Frequency curves Cummulative Frequency curves or “ogives” 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 magnitudes are to be displayed.

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

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) Veterinary College, Hebbal, Bangalore

The number of trees planted in different years is given below :

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

Years

No. of trees planted

1997

400

1998

450

1999

700

2000

750

2001

900

2002

1500

Total

4700

Simple Bar Graph

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

Divided Bar Graph

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

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) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

Frequency density Frequency density=

Frequency of the class adjustment factor

Adjustment factor of class=

Width of the 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) Veterinary College, Hebbal, Bangalore

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

20

25R Jayashree, 30 Asst.

40 Prof(AGB) 45 50 Dr. Veterinary College, Hebbal, Bangalore

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 mid-value.

• 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) Veterinary College, Hebbal, Bangalore

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

Veterinary College, Hebbal, Bangalore

Frequency Polygon

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

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) Veterinary College, Hebbal, Bangalore

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 58-63 64-69 70-75

12 5 1 2

24 29 30 32

20 8 3 2

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

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) Veterinary College, Hebbal, Bangalore

Lorenz Curve

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

Used in picturising the dispersion of wealth, sales and profits etc.

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

District

Surthi

Murrah

Bangalor e(U)

3143

370

Bangalor e速

4717

785

Belgaum

15835

5000

Bellary

2045

2995

Area Graph 25000 20000 15000

Series2 Series1

10000 5000

697

4965

476

D.Kanna da

3031

549

Dharwad

8411

635

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

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

Chitradur ga

ja pu r

324

Bi

2853

Ch i

Chickma galur

da r

642

Bi

1069

Be lla ry

Bijapur

0

lo re (U Ba ) ng al or e速 Be lg au m

1539

Ba ng a

Bidar

Symmetrical Graph

The frequencies are more or less symmetrically distributed, around a mean class Dr. R Jayashree, Asst. Prof(AGB) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

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) Veterinary College, Hebbal, Bangalore

Thank you

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