The marks obtained by 15 students out of a maximum of 25 in a test are given as 13, 11, 16, 15, 18, 12, 13, 14, 10, 22, 15, 21, 20, 17, and 24. Find the product of the modes of this set of data.

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**Solution:**

1. Identify the modes of the data set. The mode is the number that appears most frequently.

- Given data: 13, 11, 16, 15, 18, 12, 13, 14, 10, 22, 15, 21, 20, 17, 24
   - Frequency count:
     - 13 appears 2 times
     - 15 appears 2 times
     - All other numbers appear once

2. Since 13 and 15 both appear twice, they are the modes.

3. Calculate the product of the modes:

$$13 	imes 15 = 195$$

**Answer:** The product of the modes is **195**.

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