If $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $s$, then find the standard deviation of the observations $a+k$, $b+k, c+k, d+k$ and $e+k$ is

If $x_1, x_2, x_3, x_4$ and $x_5$ be the observations with mean $m$ and standard deviation $s$ then, the standard deviation of the observations $k x_1, k x_2$, $k x_3, k x_4$ and $k x_5$ is

Let $x_1, x_2, \ldots x_n$ be $n$ observations. Let $w_i=l x_i+k$ for $i=1,2, \ldots, n$, where $l$ and $k$ are constants. If the mean of $x_i$ 's is 48 and their standard deviation is 12 , the mean of $w_i{ }^{\prime} s$ is 55 and standard deviation of $w_i{ }^{\prime} s$ is 15 , then the value of $l$ and $k$ should be

The standard deviations for first natural numbers is

Consider the numbers $1,2,3,4,5,6,7,8,9$, and 10 . If 1 is added to each number the variance of the numbers, so obtained is