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Question

Draw a frequency polygon for the following frequency distribution:
Class interval11011202130314041505160Frequency8361227


Solution

Sol:

The given frequency distribution table is as below:

Class intervals 1-10 11-20 21-30 31-40 41-50 51-60
Frequency 8 3 6 12 2 7

This table has inclusive class intervals and so these are to be converted into exclusive intervals (i.e. true class limits).

These are (0.5-10.5), (10.5-20.5),(20.5-30.5),(30.5-40.5),(40.5-50.5), and (50.5-60.5).

In order to draw a frequency polygon, we need to determine the class marks. Class marks of a class interval = upper limit+lower limit2

Take imaginary class interval (-9.5 – 0.5) at the beginning and (60.5 – 70.5)  at the end, each with frequency zero. So we have the following table

Class intervals True class Intervals Class marks Frequency
(-9)-0 (-9.5)-0.5 -4.5 0
1-10 0.5-10.5 5.5 8
11-20 10.5-20.5 15.5 3
21-30 20.5-30.5 25.2 6
31-40 30.5-40.5 35.5 12
41-50 40.5-50.5 45.5 2
51-60 50.5-60.5 55.5 7
61-70 60.5-70.5 65.5 0

Now, take class marks along x-axis and their corresponding along y-axis.

Mark the points and join them.

Thus, we obtain a complete frequency polygon as shown below:

https://lh3.googleusercontent.com/NZRpUECEzto9NN8P6hxBIYX7OU50dE2SN90lc320w-ouD6SxTunMLNnV4gZ81f_UCFBtN4-0FQ5dJFSU6oEByoRBsj9Itdak3AsVMAH8OYrfYL7cMYpzj9GiQO-gbX9W63PkjJ2P

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