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.

If the data $x_1, x_2, ..., x_{10}$ is such that the mean of the first four of these is $11$,the mean of the remaining six is $16$,and the sum of squares of all of these is $2,000$; then the standard deviation of this data is

The standard deviation of the scores $505, 510, 515, 520, \ldots, 595$ is

The standard deviations of $x_i (i=1, 2, \ldots, 10)$ and $y_i (i=1, 2, \ldots, 10)$ are $a$ and $b$ respectively. $\bar{x}$ and $\bar{y}$ are the means of these two sets of observations. If $z_i = (x_i - \bar{x})(y_i - \bar{y})$ and $\sum_{i=1}^{10} z_i = c$,then the standard deviation of the observations $(x_i - y_i)$ for $i=1, 2, \ldots, 10$ is:

The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results:
Number of observations $= 25$,mean $= 18.2 \text{ seconds}$,standard deviation $= 3.25 \text{ s}$.
Further,another set of $15$ observations $x_{1}, x_{2}, \ldots, x_{15}$,also in seconds,is now available and we have $\sum_{i=1}^{15} x_{i} = 279$ and $\sum_{i=1}^{15} x_{i}^{2} = 5524$. Calculate the standard deviation based on all $40$ observations.

The standard deviation of the data $6, 7, 8, 9, 10$ is