Two groups of 15 and 22 values have variances 9 and 16 respectively. If the group means differ by 8.2, then find the standard deviation of the combined group of values.

Find the mean deviation about mean of two values x_1 and x_2 .

The mean and standard deviation of observations are 8 and 14 respectively. If each observation be multiplied by 3, the find the new and mean and new standard deviation of the resulting observation.

The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations

Find the standard deviation of the values a,a+b,a+2b,a+3b,...,a+2nb(b>0) .

The mean and variance of seven observations are 8 and 16 respectively. If five of these be 2,4,10,12, 14, find the remaining two observations.

Let x and y be two independent random variables having variance k and 2 respectively if the variance of z=3y -x be 25 find k

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 arithmetic mean of 200 values of a variable is 50. Later on, it is found that two values 92 and 8 have been taken wrongly instead of 192 and 88 respectively . After correction , find the actual arithmetic mean of the given values.

x and u are two variables with relation x= (U-15)/10 . If the mean value of u is 20, then find the mean value of x.

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14 . Find the remaining two observations.