Multiple choice

Marks distribution of 20 students of a class is as follows: Marks Number of students 0 – 5 2 5 – 10 1 10 – 15 8 15 – 20 2 20 – 25 7 What is the mode of the above given data?

  1. 12.69

  2. 12.00

  3. 17.69

  4. 18.32
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A Correct answer
Explanation

The modal class is 10-15 (frequency 8). Mode = L + ((f1 - f0) / (2*f1 - f0 - f2)) * h. L=10, f1=8, f0=1, f2=2, h=5. Mode = 10 + ((8-1) / (16-1-2)) * 5 = 10 + (7/13) * 5 = 10 + 35/13 = 10 + 2.69 = 12.69.

AI explanation

The modal class is 10 to 15, which has the highest frequency of 8. Using the empirical mode formula, Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) * h, where L is 10, f1 is 8, f0 is 1, f2 is 2, and h is 5. Calculating the fraction gives (8 - 1) / (16 - 1 - 2) = 7/13. Multiplying by 5 gives 35/13 = 2.69, which when added to 10 results in a mode of 12.69.

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