Assertion : The following is the data of wages per day : 8, 4, 7, 5, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8, then the mode of the data is 8.
Reason : Mode = Highest observation - lowest observation.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not tlie correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to determine the mode of the given data set and evaluate the assertion and reason provided.

### Step-by-Step Solution:

1. **Identify the Data**:
The given data set is:
\[ 8, 4, 7, 5, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8 \]

2. **Count the Frequency of Each Value**:
- Count how many times each number appears in the data set.
- 4 appears **1** time.
- 5 appears **3** times.
- 7 appears **3** times.
- 8 appears **4** times.
- 9 appears **2** times.
- 10 appears **1** time.

3. **Determine the Mode**:
- The mode is the number that appears most frequently in the data set.
- From our counts, the number 8 appears **4** times, which is more than any other number.
- Therefore, the mode of the data is **8**.

4. **Evaluate the Assertion**:
- The assertion states that the mode of the data is 8. Since we calculated the mode to be 8, the assertion is **true**.

5. **Evaluate the Reason**:
- The reason provided is that "Mode = Highest observation - Lowest observation."
- This statement is incorrect. The mode is defined as the most frequently occurring value in a data set, not calculated by subtracting the lowest observation from the highest observation.
- Therefore, the reason is **false**.

6. **Conclusion**:
- The assertion is true, but the reason is false. Thus, the correct evaluation is that the assertion is true, and the reason is false.

### Final Answer:
- **Assertion**: True
- **Reason**: False