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