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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 letterNumber of surnames (frequency)
1 - 46
4 - 630
6 - 844
8 - 1216
12 - 204

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 letterNumber of surnames (frequency)Width of classLength of rectangle
1 - 463\(\frac{6 × 2}{3} = 4\)
4 - 6302\(\frac{30 × 2}{2} = 30\)
6 - 8442\(\frac{44 × 2}{2} = 44\)
8 - 12164\(\frac{16 × 2}{4} = 8\)
12 - 2048\(\frac{4 × 2}{8} = 1\)


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.

image

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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