Multiple choice

For the following frequency distribution, the mode is 27.5 and the value of x is less than the frequency of modal class. | Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | --- | --- | --- | --- | --- | --- | | Number of students | 5 | 3 | 6 | x | 4 | What is the value of x?

  1. 5

  2. 4

  3. 3

  4. 2
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A Correct answer
Explanation

The mode lies in the class interval 20-30, so the modal class is 20-30 with a lower limit of 20. Using the mode formula, 27.5 = 20 + [(6 - 3) / (2 * 6 - 3 - x)] * 10, which simplifies to 7.5 = 30 / (9 - x). Solving this equation gives 9 - x = 4, which results in x = 5.

AI explanation

In a grouped frequency distribution, the modal class is the one with the highest frequency. Since the mode is 27.5, the modal class must be 20 to 30, and its frequency is 6. Using the empirical mode formula, mode equals lower limit plus f1 minus f0 divided by 2f1 minus f0 minus f2 multiplied by class size, which sets up 27.5 equals 20 plus 6 minus 3 divided by 12 minus 3 minus x multiplied by 10. Solving this yields 0.75 equals 3 divided by 9 minus x, making 9 minus x equal to 4 and x equal to 5. The value of x is 5.

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