Sum
Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram
C.I 
10  30 
30  50 
50  70  70  90  90  110  110  130  130  150 
ƒ  4  7  5  9  5  6  4 
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Solution
using histogram
C.I  ƒ 
10  30  4 
30  50  7 
50  70  5 
70  90  9 
90  110  5 
110  130  6 
130  150  4 
Steps:

 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
Without using Histogram:
Steps:
 Find the classmark (midvalue) of each given classinterval.
classmark = midvalue = `" Upper limit + Lower limit"/2`  On a graph paper, mark classmarks along Xaxis and frequencies along Yaxis.

On this graph paper, mark points taking values of classmarks along the Xaxis and the values of their corresponding frequencies along Yaxis.
 Draw line segments joining the consecutive points marked in step (3) above.
C.I. Classmark f 10  10 0 0 10  30 20 4 30  50 40 7 50  70 60 5 70  90 80 9 90  110 100 5 110  130 120 6 130  150 140 4 150  170 160 0
Concept: Graphical Representation of Data
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