# Q. 9.     100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet               in the surnames was found as follows:              (i) Draw a histogram to depict the given information.

Since the class sizes vary to make the histogram we have to calculate the weighted frequency for each rectangle as per its width

$\\Weighted\ frequency=\frac{Minimum\ class\ size}{Class\ size\ of\ the\ interval}\times Frequency\\ Length\ of\ the\ rectangle=\frac{Minimum\ width}{Width\ of\ the\ rectangle}\times Frequency$

Minimum class size = 6 - 4 = 2

The modified table showing the weighted frequency as per the size of the class intervals is as follows.

The histogram representing the information given in the above table is as follows.

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