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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: - Mathematics

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प्रश्न

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
  1. Draw a histogram to depict the given information.
  2. Write the class interval in which the maximum number of surnames lie.
आलेख
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उत्तर

(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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अध्याय 14: Statistics - Exercise 14.3 [पृष्ठ २६१]

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एनसीईआरटी Mathematics [English] Class 9
अध्याय 14 Statistics
Exercise 14.3 | Q 9 | पृष्ठ २६१

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