1. **State the problem:** We have a frequency table showing the number of students who scored each point value on a 5-point quiz. The scores are 0, 1, 2, 3, 4, and 5 points, with corresponding student counts 1, 1, 3, $x$, 8, and 3 respectively. 2. **Given:** The class average score is 3.25 points. 3. **Goal:** Find the value of $x$, the number of students who scored 3 points, and then find the total number of students in the class. 4. **Formula for average (mean):** $$\text{Average} = \frac{\sum (\text{score} \times \text{frequency})}{\sum \text{frequency}}$$ 5. **Apply the formula:** Let total students be $N = 1 + 1 + 3 + x + 8 + 3 = 16 + x$. Sum of scores times frequencies: $$1\times0 + 1\times1 + 3\times2 + x\times3 + 8\times4 + 3\times5 = 0 + 1 + 6 + 3x + 32 + 15 = 54 + 3x$$ 6. **Set up the equation for average:** $$3.25 = \frac{54 + 3x}{16 + x}$$ 7. **Solve for $x$: ** Multiply both sides by $16 + x$: $$3.25(16 + x) = 54 + 3x$$ $$52 + 3.25x = 54 + 3x$$ Subtract $3x$ from both sides: $$52 + \cancel{3.25x} - \cancel{3x} = 54$$ $$52 + 0.25x = 54$$ Subtract 52 from both sides: $$0.25x = 2$$ Divide both sides by 0.25: $$x = \frac{2}{0.25}$$ $$x = 8$$ 8. **Find total number of students:** $$N = 16 + x = 16 + 8 = 24$$ **Final answer:** There are 24 students in Dr. Hicks's class.