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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 |
- Draw a histogram to depict the given information.
- Write the class interval in which the maximum number of surnames lie.
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Solution
(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.
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