Explanation:

When all observations occur with equal frequency, it means that each observation appears the same number of times in the dataset. In such a scenario, the mode is the only measure of central tendency that exists. Let's discuss each measure of central tendency and why they may or may not exist in this situation:

Mean:
The mean is the sum of all observations divided by the total number of observations. When all observations occur with equal frequency, the sum of all observations will be the same for each observation. Since the denominator (total number of observations) is the same and the numerator (sum of observations) is the same for each observation, the mean will be the same for all observations. Therefore, the mean does not exist in this situation.

Median:
The median is the middle value in a dataset when arranged in ascending or descending order. When all observations occur with equal frequency, the dataset will be symmetrical, and every observation will be the middle value. Therefore, every observation will be the median, and all observations will have the same median.

Mode:
The mode is the value that appears most frequently in a dataset. When all observations occur with equal frequency, every observation appears the same number of times, making all observations have the same frequency. Therefore, there will be no value that appears more frequently than others, and all observations will have the same mode.

In conclusion, when all observations occur with equal frequency, the only measure of central tendency that exists is the mode. The mean does not exist because it will be the same for all observations, and the median does not exist because every observation will be the middle value.