# Mean

- The sum of the square of deviations from mean is minimum, i.e., is least.
- The sum of deviations of items from their mean is equal to zero, i.e., = 0.
- The mean is affected accordingly if the observations are given mathematical treatment by any constant item.
- The arithmetic mean is independent of origin, i.e., it is not affected by any change of origin (assumed mean).

# Median

- The sum of the absolute values of deviation of the item from median is minimum.
- It is a positional average and is not influenced by the position of the items.

# Mode

It is not affected by the presence of extremely large or small items.

# Combined standard deviation

If there are two sets of observations containing

*n*_{1}and*n*_{2}items with respective mean and standard deviations Ïƒ_{1}and Ïƒ_{2}, then the mean and standard deviation of the*n*_{1}+*n*_{2}observations, taken together, is