Multiple choice

A test was conducted for the students of Class X in a school for 14 students which resulted in the following frequency table for the marks obtained by the 14 students: | Marks Obtained | 0-10 | 10-20 | 20-30 | | --- | --- | --- | --- | | Number of students | 4 | 8 | 2 | Find the mode of the given data.

  1. 10

  2. 14

  3. 18

  4. 24
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B Correct answer
Explanation

The modal class is 10-20 (highest frequency 8). Mode = L + ((f1 - f0) / (2*f1 - f0 - f2)) * h. L=10, f1=8, f0=4, f2=2, h=10. Mode = 10 + ((8-4) / (16-4-2)) * 10 = 10 + (4/10) * 10 = 14.

AI explanation

Using the formula for the mode of grouped data, Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) multiplied by h. The modal class is 10-20, so L = 10, f1 = 8, f0 = 4, f2 = 2, and h = 10. Substituting these values gives Mode = 10 + ((8 - 4) / (16 - 4 - 2)) times 10, which simplifies to 10 + (4/10) times 10, yielding 14.

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