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# 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 sumames was found as follows:

**(i)** Draw a histogram to depict the given information.

**(ii)** Write the class interval in which the maximum number of surnames lie."

Given:

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.

To do:

We have to

(i) Draw a histogram to depict the given information.

(ii) Write the class interval in which the maximum number of surnames lie.

Solution:

(i) The width of the class intervals in the given data is varying.

We know that,

The area of rectangle is proportional to the frequencies in the histogram.

This implies,

The proportion of the number of surnames per 2 letters interval can be calculated as given in the below table:

Let the x-axis represent the number of letters and the y-axis represent the proportion of the surnames per 2 letters interval.

The required histogram is as follows:

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