1. **State the problem:** We need to evaluate the expression $$x^2 = \sum \frac{(23.25 - 6.5)^2}{6.5}$$ where the summation symbol $\sum$ here implies a single term since no index or multiple terms are given. 2. **Understand the formula:** This looks like a chi-square component formula where each term is $$\frac{(O - E)^2}{E}$$ with observed value $O = 23.25$ and expected value $E = 6.5$. 3. **Calculate the numerator:** $$ (23.25 - 6.5)^2 = (16.75)^2 = 280.5625 $$ 4. **Calculate the denominator:** $$ 6.5 $$ 5. **Form the fraction:** $$ \frac{280.5625}{6.5} $$ 6. **Simplify the fraction:** $$ \frac{\cancel{280.5625}}{\cancel{6.5}} = 43.1634615385 $$ (rounded to 10 decimal places) 7. **Final answer:** $$ x^2 = 43.1635 $$ (rounded to 4 decimal places) This is the value of the given expression.