12. ___, 1 3/4, 2, 3 1/5, 4 1/4 range = 2 3/4

Explanation:

Step1: Recall range formula

The range of a data - set is given by $Range = \text{Max}-\text{Min}$. We know the range and the maximum value, and we need to find the minimum value. Let the missing number (minimum value) be $x$. The maximum value in the data - set is $4\frac{1}{4}=\frac{17}{4}$, and the range is $2\frac{3}{4}=\frac{11}{4}$.

Step2: Set up the equation

Using the range formula $\frac{11}{4}=\frac{17}{4}-x$.

Step3: Solve for x

Add $x$ to both sides: $x + \frac{11}{4}=\frac{17}{4}$. Then subtract $\frac{11}{4}$ from both sides: $x=\frac{17}{4}-\frac{11}{4}$.

Step4: Calculate the value of x

$x=\frac{17 - 11}{4}=\frac{6}{4}=1\frac{1}{2}$.

Answer:

$1\frac{1}{2}$