100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letter in English alphabet in the surnames 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.

Explanation

(i) We know that, the areas of the rectangles are proportional to the frequencies in a histogram. Here, the widths of the rectangles are varying. So, we need to make certain modifications in the lengths of the rectangle. So that the areas are again proportional to the frequencies.
1 Select a class interval with the minimum class size. The minimum class size is 2.
2. The lengths of the rectangles are then modified to be proportionate to the class-size 2.
Since, we have calculated these lengths for interval of 2 letters in each case, we may call these lengths as 'proportion of surnames per 2 mark interval'.
So, the correct histogram with varying width is given below:
Here, we make a modified table by given data with minimum class-size 2


(ii) The class interval in which the maximum number of surnames lie is 6-8.