Question

Draw a frequency polygon for the following frequency distribution: Class interval1−1011−2021−3031−4041−5051−60Frequency8361227

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:

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