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Mathematics

The following table shows the number of illiterate persons in the age group (10 - 69) in a town

Age group (in years)No. of illiterate persons
10 - 1950
20 - 29125
30 - 39190
40 - 49275
50 - 59340
60 - 69410

Draw a histogram to represent the above data.

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 class2=20192=12=0.5\Rightarrow \text{Adjustment factor} = \dfrac{\text{Lower limit of one class - Upper limit of previous class}}{2} \\[1em] = \dfrac{20 - 19}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 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 the given data is :

Age group before adjustmentAge group after adjustmentNo. of illiterate persons (Frequency)
10 - 199.5 - 19.550
20 - 2919.5 - 29.5125
30 - 3929.5 - 39.5190
40 - 4939.5 - 49.5275
50 - 5949.5 - 59.5340
60 - 6959.5 - 69.5410

Steps of construction :

  1. Take 2 cm along x-axis = 10 years

  2. Take 1 cm along y-axis = 50 units

  3. A kink is drawn near x-axis to show that the scale starts from 9.5 and not zero.

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

The required histogram is shown in the below figure:

The following table shows the number of illiterate persons in the age group (10 - 69) in a town. Graphical Representation of Statistical Data, RSA Mathematics Solutions ICSE Class 10.

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