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 4 - 6 6 - 8 8 - 12 12 - 20 |
6 30 44 16 4 |
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surname lie.
(i) The class intervals in the data is having varying width. We know that the area of rectangle is proportional to the frequencies in the histogram. The class interval with minimum class size 2 is selected and the length of the rectangle is proportionate to it.
The proportion of the surnames per 2 letters interval can be calculated as:
| Number of letters | Number of surnames | Width of class | Length of rectangle |
| 1-4 | 6 | 3 | (6/3)×2 = 4 |
| 4-6 | 30 | 2 | (30/2)×2 = 30 |
| 6-8 | 44 | 2 | (44/2)×2 = 44 |
| 8-12 | 16 | 4 | (16/4)×2 = 8 |
| 12-20 | 4 | 8 | (4/8)×2 = 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.
(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.
