# Mean

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

# Median

1. The sum of the absolute values of deviation of the item from median is minimum.
2. 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 n1 and n2 items with respective mean and standard deviations Ïƒ1 and Ïƒ2, then the mean and standard deviation of the n1 + n2 observations, taken together, is