Properties of arithmetic mean

Answer 1

Some properties of Arithmetic mean

• If x 1 and x2 are the means of the two groups computed from the values n1 and n2 then the mean x is given by the formula

  x = n1x1+n2x2/ n1+n2

• If each observation in the data is replaced by x, the sum total of all the observations remains unchanged.

  x = x1,x2,x3,x4........,xn/n

  So x1,x2,x3,x4........,xn = nx

  Replacing each observation by x, we get

  x+x+x........+x = nx

• If every value of the variable x is either increased, decreased, divided or multiplied by a constant, the observations so obtained also increases, decreases, gets multiplied or gets divided respectively by the same constant.
• Algebraic sum of the deviation of a set of values from their arithmetic mean is 0