The correct answer is (a) Arithmetic Mean.
The arithmetic mean is the sum of a list of numbers divided by the number of numbers in the list. It is often denoted by $\mu$ or $\bar{x}$.
The median is the middle value in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the arithmetic mean. It is often denoted by $M$.
The geometric mean is the product of the elements of a list, and is equal to the nth root of the product of the n elements. It is often denoted by $GM$.
The mode is the value that appears most often in a set of data. It is often denoted by $\mu_0$.
The sum of the absolute deviations is minimum when deviations are taken from the arithmetic mean. This is because the arithmetic mean is the most representative value of a set of data. When deviations are taken from the arithmetic mean, the sum of the absolute deviations is equal to the variance of the data set. The variance is a measure of how spread out the data are. A low variance indicates that the data are close to the mean, while a high variance indicates that the data are spread out over a large range of values.
The median is not always the best measure of central tendency. For example, if a data set contains two numbers that are very different from the other numbers in the set, the median will be closer to the average of the two extreme numbers than to the average of the entire set. This can make the median a less representative value of the data set.
The geometric mean is not always the best measure of central tendency. For example, if a data set contains negative numbers, the geometric mean will be negative. This can make the geometric mean a less representative value of the data set.
The mode is not always the best measure of central tendency. For example, if a data set contains two numbers that are very different from the other numbers in the set, the mode will be the value that appears twice, even though the other numbers in the set may be more representative of the data set.
Therefore, the sum of the absolute deviations is minimum when deviations are taken from the arithmetic mean.