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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 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.

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(i) Here, it can be observed that the data has class intervals of varying width. The proportion of the number of surnames per 2 letters interval can be calculated as follows. Number of letters Frequency (Number of surnames) Width of class Length of rectangle 1 − 4 6 3 4 − 6 30 2 ...
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(i) Here, it can be observed that the data has class intervals of varying width. The proportion of the number of surnames per 2 letters interval can be calculated as follows.

Number of letters Frequency (Number of surnames) Width of class
Length of rectangle
1 − 4 6 3  
4 − 6 30 2  
6 − 8 44 2  
8 − 12 16 4  
12 − 20 4 8  

 

By taking the number of letters on x-axis and the proportion of the number of surnames per 2 letters interval on y-axis and choosing an appropriate scale (1 unit = 4 students for y axis), the histogram can be constructed as follows.

 

(ii) The class interval in which the maximum number of surnames lies is 6 − 8 as it has 44 surnames in it i.e., the maximum for this data.

 
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