Given the quadratic equation \(x^2 - 2sx + n = 0\) where \(s\) is the sample mean of a dataset \(a, b, c\) and \(n\) is the perfect square trinomial. Find the value of \(n\) if the dataset is \(3, 5, 7\).

Step 1 ：Step 1: Calculate the sample mean \(s\) of the dataset \(3, 5, 7\) using the formula \(s = \frac{a+b+c}{3}\).

Step 2 ：Step 2: Substitute \(a = 3\), \(b = 5\), and \(c = 7\) into the formula to get \(s = \frac{3+5+7}{3} = 5\).

Step 3 ：Step 3: Since the sample mean \(s\) is 5, the quadratic equation becomes \(x^2 - 2*5x + n = 0\) or \(x^2 - 10x + n = 0\).

Step 4 ：Step 4: To form a perfect square trinomial, \(n\) must be equal to \(\left(\frac{b}{2}\right)^2\) where \(b\) is the coefficient of \(x\) in the quadratic equation.

Step 5 ：Step 5: Substitute \(b = -10\) into the formula to get \(n = \left(\frac{-10}{2}\right)^2 = 25\).