# Average

Average or Mean =

# Variance and standard deviation

• The variance of a variate X is the arithmetic mean of the squares of all deviations of X from the arithmetic mean of the observations and is denoted by Var (X) or Ïƒ2
• The positive square root of the variance of a variate X is known as standard deviation. i.e.,
• To calculate the sum of quantities, they should be in the same unit.
• Average of a group consisting two different groups when their averages are known:

Let Group A contains m quantities and their average is a and Group B contains n quantities and their average is b, then average of group C containing a + b quantities
• If, in a group, one or more new quantities are added or excluded, then the new quantity or sum of added or excluded quantities = [Change in no. of quantities Ã— original average] Â± [change in average Ã— final no. of quantities]

Take +ve sign if quantities added and take â€“ve sign if quantities removed.