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Mathematics

Draw an ogive for the following frequency distribution :

Class-intervalsFrequency
1 - 103
11 - 205
21 - 308
31 - 407
41 - 506
51 - 602

Measures of Central Tendency

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Answer

To draw an ogive :

  1. The given frequency distribution is discontinuous, to convert it into continuous distribution,
    Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2
    =11102=12=0.5= \dfrac{11 - 10}{2} = \dfrac{1}{2} = 0.5

The cumulative frequency table for the given data is :

Classes before adjustmentClasses after adjustmentFrequencyCumulative frequency
1 - 100.5 - 10.533
11 - 2010.5 - 20.558
21 - 3020.5 - 30.5816
31 - 4030.5 - 40.5723
41 - 5040.5 - 50.5629
51 - 6050.5 - 60.5231
  1. Since, the scale on x-axis starts at 0.5, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 0.5

  2. Take 2 cm along x-axis = 10

  3. Take 1 cm along y-axis = 5

Draw an ogive for the following frequency distribution. Measures of Central Tendency, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.
  1. Plot the points (10.5, 3), (20.5, 8), (30.5, 16), (40.5, 23), (50.5, 29), (60.5, 31) representing upper class limits and the respective cumulative frequencies.

Also plot the point representing lower limit of the first class i.e. 0.5 - 10.5

  1. Join these points by a freehand drawing.

The required ogive is shown in figure above.

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