If mean of squares of deviations of a set of n observations about -2 and 2 are 18 and 10 respectively, then standard deviation of this set of observations is

The mean square deviations of a set of observations x_(1),x_(2), …, x_(n) about a point c is defined to be (1)/(n) sum_(i=1)^(n)(x_(i)-c)^(2) . The mean square deviations about -1 and +1 of a set of observations are 7 and 3, repectively. Find the standard deviation of this set of observations.

The mean square deviation of a set of observation x_(1), x_(2)……x_(n) about a point m is defined as (1)/(n)Sigma_(i=1)^(n)(x_(i)-m)^(2) . If the mean square deviation about -1 and 1 of a set of observation are 7 and 3 respectively. The standard deviation of those observations is

If standard deviation of a set of observation is 4 and if each of the observations is divided by 4, then the standard deviation of new set of observations is

The mean and standard deviation of a set of n_1, observations are bar x_1 and s_1 ,respectively while the mean and standard deviation of another set of n_2 observations are bar x_2 and s_2, respectively. Show that the standard deviation of thecombined set of (n_1 + n_2) observations is given by S.D.=sqrt((n_1(s_1)^2+n_2(s_2)^2)/(n_1+n_2)+(n_1 n_2(( bar x )_1-( bar x )_2)^2)/((n_1+n_2)^2))

If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if (i) each observation is multiplied by 5. (ii) 7 is added to each observation.