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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 letter | Number of surnames (frequency) |
| 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 :
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 letter | Number of surnames (frequency) | Width of class | Length of rectangle |
| 1 - 4 | 6 | 3 | \(\frac{6 × 2}{3} = 4\) |
| 4 - 6 | 30 | 2 | \(\frac{30 × 2}{2} = 30\) |
| 6 - 8 | 44 | 2 | \(\frac{44 × 2}{2} = 44\) |
| 8 - 12 | 16 | 4 | \(\frac{16 × 2}{4} = 8\) |
| 12 - 20 | 4 | 8 | \(\frac{4 × 2}{8} = 1\) |
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.
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.