4. 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 .
8. Following steps are necessary to plot
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.
9. 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.
10. 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 .
11. 3. Plot the points x, y, where is the upper
limit of the class and y is the
corresponding cumulative frequency.
4. Joins the points by a smooth curve.
14. 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.
15. •Be easily understood due to
widespread use in business and
media.
•Show the number of proportion
or of data point above / below
a particular value.
•Become more smooth as data
points or classes added.
16.
17. Ogive can:
•Fail to reflect all data points in a data set.
•Be somewhat complicated to prepare.
•Reveal little about central
tendency, dispersion , skew
or kurtosis.
18. • 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.
19.
20. For the data given below , construct a
less than cumulative frequency table
and plot its ogive .
MAR
KS
0-10 10-
20
20-
30
30-
40
40-
50
50-
60
60-
70
70-
80
80-
90
90-
100
FREQ
UENC
Y
3 5 6 7 8 9 10 12 6 4
21.
22. 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
To plot an ogive we need class boundaries and the cumulative frequencies. For grouped data ,ogive is formed by plotting the cumulative frequency against the upper boundary of the class. For ungrouped data cumulative frequency is plotted on the y-axis against the data which is on the x- axis.
An ogive is a line graph where the bases are the class boundaries and the heights are the <cf for the less than ogive and >cf for the greater than ogive.
