To make your sample mean and variance _exactly_ equal to a pre-specified value, you can appropriately shift and scale the variable. Specifically, if $X_1, X_2, ..., X_n$ is a sample, then the new variables 

$$ Z_i = \sqrt{c_{1}} \left( \frac{X_i-\overline{X}}{s_{X}} \right) + c_{2} $$ 

where $\overline{X} = \frac{1}{n} \sum_{i=1}^{n} X_i$ is the sample mean and $ s^{2}_{X} =  \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \overline{X})^2$ is the sample variance are such that the sample mean of the $Z_{i}$'s is exactly $c_2$ and their sample variance is exactly $c_1$. A similarly constructed example can restrict the range - shift/scale the data so that it lies within $(0,1)$ then multiply by $a$ and add $b$ to get it to lie in the interval $(a,b)$.