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Mathematics

Construct a frequency polygon for the following data :

Class-intervals10 - 1415 - 1920 - 2425 - 2930 - 34
Frequency581294

Statistics

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Answer

The given class interval are inclusive. For constructing polygon we will first convert them into the exclusive form.

Class - intervalsFrequencyClass marks
4.5 - 9.504.5+9.52=7\dfrac{4.5 + 9.5}{2} = 7
9.5 - 14.559.5+14.52=12\dfrac{9.5 + 14.5}{2} = 12
14.5 - 19.5814.5+19.52=17\dfrac{14.5 + 19.5}{2} = 17
19.5 - 24.51219.5+24.52=22\dfrac{19.5 + 24.5}{2} = 22
24.5 - 29.5924.5+29.52=27\dfrac{24.5 + 29.5}{2} = 27
29.5 - 34.5429.5+34.52=32\dfrac{29.5 + 34.5}{2} = 32
34.5 - 39.5034.5+39.52=37\dfrac{34.5 + 39.5}{2} = 37

Steps:

  1. Find the class-mark (mid-value) of each given class-interval.

    Class-mark = mid-value = Upper limit + Lower limit2\dfrac{\text{Upper limit + Lower limit}}{2}

  2. On a graph paper, mark class-marks along x-axis and frequencies along y-axis.

  3. On this graph paper, mark points taking values of class-marks along x-axis and the values of their corresponding frequencies along y-axis.

  4. Draw line segments joining the consecutive points marked in step (3) above.

Construct a frequency polygon for the following data : Statistics, Concise Mathematics Solutions ICSE Class 9.

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