The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if $$\alpha$$ and $$\sqrt \beta $$ are the mean and standard deviation respectively for correct data, then ($$\alpha$$, $$\beta$$) is :

Let the mean and variance of the frequency distribution

$$\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr } $$

be 6 and 6.8 respectively. If x₃ is changed from 8 to 7, then the mean for the new data will be :

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $${{37} \over 4}$$

respectively, then (a $$-$$ b)² is equal to :

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $$\sqrt {13.44} $$, then the standard deviation of the second sample is :