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Mathematics

Draw a histogram for the following data :

ClassesFrequency
59 - 6510
66 - 725
73 - 7925
80 - 8615
87 - 9330
94 - 10010

Statistics

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Answer

The following frequency distribution is discontinuous, to convert it into continuous frequency distribution,

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

= 66652=12\dfrac{66 - 65}{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.

Continuous frequency distribution for given data is :

Classes before adjustmentClasses after adjustmentFrequency
59 - 6558.5 - 65.510
66 - 7265.5 - 72.55
73 - 7972.5 - 79.525
80 - 8679.5 - 86.515
87 - 9386.5 - 93.530
94 - 10093.5 - 100.510

Steps of construction of histogram :

  1. Since, the scale on x-axis starts at 58.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 58.5

  2. Take 2 cm along x-axis = 7 units.

  3. Take 1 cm along y-axis = 5 units.

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

The required histogram is shown in the adjoining figure.

Draw a histogram for the following data. Statistics, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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