The mean of the following data is :

Question

Accepted Answer

The mean of a data set is calculated by summing all the values in the data set and then dividing by the number of values. In this case, we are given that the correct answer is Option 3, which is 16. Let's explore why this is the correct answer and why the other options are incorrect.

1. **Explanation for Option 3 (Correct Answer):**
   - The mean is calculated as the total sum of all data points divided by the number of data points. Although the specific data set is not provided in the question, we are instructed to accept that the mean is 16. This implies that when the data points are summed and divided by their count, the result is 16. Therefore, Option 3 is correct because it accurately represents the mean of the given data set.

2. **Explanation for why Option 1 (14) is incorrect:**
   - If the mean were 14, it would mean that the total sum of the data points divided by their count equals 14. However, since we are given that the correct mean is 16, a mean of 14 does not accurately represent the data set. Thus, Option 1 is incorrect.

3. **Explanation for why Option 2 (15) is incorrect:**
   - Similarly, if the mean were 15, the total sum of the data points divided by their count would equal 15. However, the correct mean is specified as 16, so a mean of 15 does not match the given information. Therefore, Option 2 is incorrect.

4. **Explanation for why Option 4 (18) is incorrect:**
   - If the mean were 18, it would imply that the total sum of the data points divided by their count equals 18. Since the correct mean is 16, a mean of 18 is not consistent with the provided data. Hence, Option 4 is incorrect.

In conclusion, Option 3 is the correct answer because it aligns with the given information that the mean of the data set is 16. The other options do not match this value and are therefore incorrect.