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

1. Draw a histogram to depict the given information.
2. 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	`(6 xx 2)/3` = 4
4 − 6	30	2	`(30 xx 2)/2` = 30
6 − 8	44	2	`(44 xx 2)/2` = 44
8 − 12	16	4	`(16 xx 2)/4` = 8
12 − 20	4	8	`(4 xx 2)/8` = 1

By taking the number of letters on the x-axis and the proportion of the number of surnames per 2 letters interval on the y-axis and choosing an appropriate scale (1 unit = 4 students for the 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.