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

Consider the first 10 positive integers. If we multiply each number by $-$1 and, then add 1 to each number, the variance of the numbers, so obtained is

The following information relates to a sample of size 60, $\Sigma x^2=18000$, and $\Sigma x=960$. Then, the variance is