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Mathematics

Draw histograms for the following frequency distributions :

Class intervalFrequency
30 - 3924
40 - 4916
50 - 5909
60 - 6915
70 - 7920

Statistics

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Answer

The above distribution is discontinuous, converting into continuous distribution, we get :

Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

= 40392=12\dfrac{40 - 39}{2} = \dfrac{1}{2}

= 0.5

Subtract the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.

Classes before adjustmentClasses after adjustmentFrequency
30 - 3929.5 - 39.524
40 - 4939.5 - 49.516
50 - 5949.5 - 59.509
60 - 6959.5 - 69.515
70 - 7969.5 - 79.520

Steps of construction of histogram :

  1. Since, the scale on x-axis starts at 29.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 29.5.

  2. Take 2 cm along x-axis = 10 units.

  3. Take 2 cm along y-axis = 5 units.

  4. Construct rectangles corresponding to the above continuous frequency distribution table.

The required histogram is shown in the below figure:

Draw histograms for the following frequency distributions. Graphical Representation, Concise Mathematics Solutions ICSE Class 10.

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