Question

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:

Number of letters	Number of surnames
1 − 4	6
4 − 6	30
6 − 8	44
8 − 12	16
12 − 20	4

(i) Draw a histogram to depict the given information. 
(ii) Write the class interval in which the maximum number of surnames lie.

Answer 1

(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	\(\frac{6\times 2}{3}=4\)
4 − 6	30	2	\(\frac{30\times 2}{2}=30\)
6 − 8	44	2	\(\frac{44\times 2}{2}=44\)
8 − 12	16	4	\(\frac{16\times 2}{4}=8\)
12 − 20	4	8	\(\frac{4\times 2}{8}=1\)

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.    
 

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(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.