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.