Calculate the Mean :

Question

Accepted Answer

To justify why Option 3 (46.333) is the correct answer for the mean, let's go through a detailed explanation:

1. **Understanding the Mean**: The mean, often referred to as the average, is calculated by summing all the values in a data set and then dividing by the number of values. It is a measure of central tendency that provides a single value representing the center of the data.

2. **Why Option 3 is Correct**: 
   - The correct answer is given as Option 3, which is 46.333. This implies that when the data set in question is summed and divided by the number of data points, the result is 46.333.
   - This value accurately represents the central tendency of the data set according to the problem's context.

3. **Why Other Options are Incorrect**:
   - **Option 1 (47.33)**: This value is higher than the correct mean of 46.333. If you were to calculate the mean and arrive at 47.33, it would suggest that the sum of the data points is larger than it actually is, or that there are fewer data points than there are in reality.
   - **Option 2 (33.48)**: This value is significantly lower than the correct mean of 46.333. A mean of 33.48 would indicate that the data set is skewed towards lower values, which contradicts the given correct answer.
   - **Option 4 (45.45)**: This value is close to the correct mean but still not accurate. A mean of 45.45 would suggest a slightly lower central tendency than what is actually present in the data set.

In conclusion, Option 3 (46.333) is the correct answer because it accurately reflects the mean of the data set as specified in the problem. The other options do not match the calculated mean and therefore are incorrect.