Ogive and its application

1. OGIVES

2. MEANING
Cumulative histogram also known as ogives , are
graph that can be used to determine how many data values
lie above or below a particular value in a data set .

4. OGIVE

6. Following steps are necessary to plot a less than
type ogive curve.
1. Start from the upper limit of the class intervals
and then add class frequency to the cumulative
frequency distribution.
2. Take upper in the x-axis direction cumulative
frequencies along the y-axis direction.
3. Plot the points ( x,y ) , where is the upper limit
of the class and y is the corresponding
cumulative frequency.
4. Join the points by a smooth curve.

7. Following steps are necessary to plot a more than
type ogive curve ;
1. Starts from the lower limit of the class
intervals and total frequency is subtracted
from the frequency to get the cumulative
frequency distribution .
2. In the graph , consider the lower limit x - axis
direction and cumulative frequencies along y -
axis direction .
3. Plot the points( x,y) ,where 'x' is the lower limit
of the class and 'y' is the corresponding
cumulative frequency .
4. Join the points by a smooth curve.

8. Advantages and
Disadvantages of
Ogive

9. ADVANTAGES
Ogive can
visually approximate
summarize a large data set in visual form

10. delineate each interval in the frequency
distribution
clarify rates of change between classes better
than other graph
provide visual check of accuracy or
reasonableness of calculations

11.  become more smooth as data points or classes
added
 be easily understood due to widespread use in
business and media
 show the number of proportion of data point
above / below a particular value

12. Disadvantages

13.  Ogive can:
 Be somewhat complicated to prepare
 fail to reflect all data points in a data set
 reveal little about central tendency, dispersion , skew or
kurtosis

14.  often requires additional written or written or verbal
explanation
 be inadequate to describe to attribute, behaviour, or
condition of interest
 fail to reveal key assumptions

15. SOLVED
EXAMPLES

16. QUESTION : For the data given below , construct a less than cumulative
frequency table and plot its ogive .
MARKS 0-10 10-
20
20-
30
30-
40
40-
50
50-
60
60-
70
70-
80
80-
90
90-
100
FREQUE
NCY
3 5 6 7 8 9 10 12 6 4

17. SOlUTION
MARKS FREQUENCY LESS THAN CUMULATIVE
FREQUENCY
0-10 3 3
10-20 5 8
20-30 6 14
30-40 7 21
40-50 8 29
50-60 9 38
60-70 10 48
70-80 12 60
80-90 6 66
90-100 4 70

19. MARK
S
0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50
FREQ
UENC
Y
3 5 7 8 10 11 14 19 15 13
QUESTION: For the data given below,
construct more than cumulative frequency
and plot ita ogive

20. MARKS FREQUENCY CUMULATIVE
FREQUENCY
0-5 3 95
5-10 5 95-3 = 92
10-15 7 92-5 = 87
15-20 8 87-7 = 80
20-25 10 80-8 =72
25-30 11 72-10 = 62
30-35 14 62-11 = 51
35-40 19 51-14 = 37
40-45 15 37-19 = 18
45-50 13 18-15 = 3
SOLUTION

22. REFERENCES
 https://www.statisticshowto.datasciencecentral.com/ogive-graph
 /https://www.statisticshowto.datasciencecentral.com/ogive-graph/
 http://www.mathcaptain.com/statistics/ogive.html
 www.preciousheart.net/chaplaincy/Auditor_Manual/11grphd.pdf