If the mean and the median pertaining to a certain character of a population are of the same value, the following is most likely to occur:-

Options

A. normal distribution
B. bi-modal distribution
C. T-shaped curve
D. skewed curve

Explanation

To solve the question regarding the relationship between the mean and median in a population, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mean and Median**:
- The mean is the average of all data points in a population, calculated by summing all values and dividing by the number of values.
- The median is the middle value when all data points are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.

2. **When Mean Equals Median**:
- When the mean and median are equal, it often indicates a symmetrical distribution of data. This is commonly seen in normal distributions (bell-shaped curves).

3. **Implications of Symmetrical Distribution**:
- In a symmetrical distribution, the data is evenly distributed around the mean/median. This means that there are no extreme outliers skewing the data in one direction.

4. **Conclusion**:
- If the mean and median are the same, it is most likely that the population follows a normal distribution or is symmetrically distributed.

### Final Answer:
If the mean and the median pertaining to a certain character of a population are of the same value, the population is most likely to be symmetrically distributed.