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

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CASE_STUDIESHistogram with Varying Class WidthsNCERT Textbook2 sub-questions

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To draw a histogram to represent the following frequency distribution: | Class interval | 5–10 | 10–15 | 15–25 | 25–45 | 45–75 | |----------------|------|-------|-------|-------|-------| | Frequency | 6 | 12 | 10 | 8 | 15 | The adjusted frequency for the class 25–45 is

MCQ (Single)Histogram with Varying Class Widths

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 - 20, 20 - 30, . . ., 60 - 70, 70 - 100. Then she formed the following table: | Marks | Number of students | |-------|--------------------| | 0 - 20 | 7 | | 20 - 30 | 10 | | 30 - 40 | 10 | | 40 - 50 | 20 | | 50 - 60 | 20 | | 60 - 70 | 15 | | 70 - above | 8 | | Total | 90 | Draw a histogram to represent the given data.

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