The most common value in a series can be determined by finding the mode. The mode is the value that appears most frequently in a set of data. It is the value that occurs with the highest frequency.

Mode:
The mode is the value that appears most frequently in a set of data. It is the value that occurs with the highest frequency. For example, if we have a series of numbers: 2, 4, 6, 4, 8, 10, 4, the mode would be 4 because it appears three times, which is more than any other number in the series.

Median:
The median is the middle value of a set of data when the values are arranged in ascending or descending order. In order to find the median, the data must be sorted first. Once the data is sorted, the median is the value that falls exactly in the middle. For example, if we have a series of numbers: 2, 4, 6, 8, 10, the median would be 6 because it is the middle value.

Arithmetic Mean:
The arithmetic mean, also known as the average, is calculated by adding up all the values in a set of data and dividing the sum by the number of values. For example, if we have a series of numbers: 2, 4, 6, 8, 10, the arithmetic mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.

All of these:
The most common value in a series can be any of the three - mode, median, or arithmetic mean. It depends on the data set and the distribution of values. In some cases, the mode might be the most common value, while in others, it could be the median or the arithmetic mean. It is important to analyze the data and calculate these measures to determine the most common value accurately.

In conclusion, the most common value in a series can be determined by finding the mode, which is the value that appears most frequently. However, it can also be the median or the arithmetic mean, depending on the data set. Therefore, the correct answer is "All of these."