If `barx_1` and `barx_2` are the A.M. of two sets with `n_1` and `n_1` observation respectively, then prove that combined mean for two sets `(barx)` lies between `barx_1` and `barx_2`.

If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c respectively, prove that, (1)/(x) + (1)/(y) = (2)/(b)

Prove that (n !+1) is not divisible by any natural number between 2 and n

If a is the A.M. of b and c and the two geometric mean are G_1 and G_2, then prove that G_1^3+G_2^3=2a b c

The AM of 1,2,…….,n with frequencies 1^2 , 2^2 ,……. n^2 respectively is

If the mean and variance of one set of values be barx_1 and s_1^2 and those of another set be barx_2 and s_2^2 respectively and each set has values 2, then prove that the variance (s^2) of the combined set of values is given by 4s^2 = 2(s_1^2 + s_2^2) + d^2 where d = (barx_1 - barx_2) .

The A.M of the series 1, 2, 4, 8, 16…., 2^n is

The mean of n observation is a. If the 1st observation is increased by 1, second by 2 and so on, then new mean is

If n is even number, then median is the mean of (n/2) th and (n/2 - 1) th observation.

If x prop y+z , y propz+x and z prop x+y , and the constant of variation are 1,m,n respectively, then prove that, l/(l+1)+m/(m+1)+n/(n+1) = 1

If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers , then prove that the value of q can not lie between p and ((n+1)/(n-1))^2p .