The mode of the following data is :
4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 6, 8, 8, 7, 7

Question

Accepted Answer

The mode of a data set is the value that appears most frequently. In the given data set:

4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 6, 8, 8, 7, 7

We need to determine which number appears the most frequently.

1. **Counting the occurrences:**
   - The number 4 appears 2 times.
   - The number 5 appears 1 time.
   - The number 6 appears 3 times.
   - The number 7 appears 4 times.
   - The number 8 appears 3 times.
   - The number 9 appears 1 time.
   - The number 10 appears 1 time.

2. **Identifying the mode:**
   - The number 7 appears 4 times, which is more frequent than any other number in the data set.

Therefore, the mode of the data set is 7, which corresponds to Option 2.

**Explanation for why each of the other options is incorrect:**

- **Option 1 (6):** The number 6 appears 3 times in the data set. While it is frequent, it is not the most frequent number. The number 7 appears more often, with 4 occurrences.

- **Option 3 (8):** The number 8 also appears 3 times, similar to the number 6. However, it is not the most frequent number since the number 7 appears 4 times.

- **Option 4 (9):** The number 9 appears only once in the data set, making it one of the least frequent numbers. It cannot be the mode since the mode is defined as the number that appears most frequently.

In conclusion, Option 2 is the correct answer because the number 7 appears more frequently than any other number in the data set.