The mean is the most common and easiest to understand indicator of the measure of central tendency.

The formula for calculating the arithmetic mean is as follows.

The mean, which is the preferred choice when considering the measure of central tendency, is the most responsive, objective and representative when compared to the median and the mode. Additionally, the mean allows for algebraic manipulation. For example, when a constant is added to each observation, an identical constant is added to the mean as well. And when each observation is multiplied by a constant, the arithmetic mean is also multiplied by an identical constant.

However, the representativeness of the mean is somewhat compromised if there are extreme values in the data.

The median divides the data into 2 halves with the same amount, one half smaller than it, while the other larger than it.

If the total of the data(n) is odd, and the number in the middle, the one in the position of (n+1)/2, is not equal to its neighbors, then it would become the median. If n is even, the mean of the 2 numbers in the middle(the two in the position of n/2 and n/2+1) would become the median, usually. If there exists several same numbers in the middle of the ordered data, in principle, they should be considered as a continuum, and use interpolation method to calculate the median by the accurate boundaries of that number.

The median only relates to the position in the data group, so it is not sensitive enough to the changes in data, but in the same time, the median is not easy to be affected by extreme numbers. The median cannot perform algebra calculations.

The mode is the number or genre to be most frequently appear, usually noted as M0. There may exist more than 1 modes in a data series.

The mode is also not easy to be affected by extreme numbers, but its representativeness is weaker than median, and it also cannot perform algebra calculations, so the mode is less used in analysis.