1. The problem presents data on "Days Missed" and "Semester Grade" for students and asks us to analyze or interpret this data. 2. A common approach is to explore the relationship between days missed and semester grade, often using correlation or regression analysis. 3. The formula for the Pearson correlation coefficient $r$ between two variables $x$ and $y$ is: $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$ where $n$ is the number of data points. 4. We combine the two sets of data into one list of pairs $(x_i, y_i)$ where $x_i$ is days missed and $y_i$ is semester grade: $(8,70), (3,84), (2,92), (10,72), (6,72), (7,81), (1,95), (13,71), (11,69), (4,80), (1,98), (13,68), (4,91), (6,72), (3,91), (5,78), (12,70), (3,89), (6,76), (2,94)$ 5. Calculate sums: $\sum x = 8+3+2+10+6+7+1+13+11+4+1+13+4+6+3+5+12+3+6+2 = 116$ $\sum y = 70+84+92+72+72+81+95+71+69+80+98+68+91+72+91+78+70+89+76+94 = 1441$ $\sum x^2 = 8^2+3^2+2^2+10^2+6^2+7^2+1^2+13^2+11^2+4^2+1^2+13^2+4^2+6^2+3^2+5^2+12^2+3^2+6^2+2^2 = 812$ $\sum y^2 = 70^2+84^2+92^2+72^2+72^2+81^2+95^2+71^2+69^2+80^2+98^2+68^2+91^2+72^2+91^2+78^2+70^2+89^2+76^2+94^2 = 105,927$ $\sum xy = 8*70 + 3*84 + 2*92 + 10*72 + 6*72 + 7*81 + 1*95 + 13*71 + 11*69 + 4*80 + 1*98 + 13*68 + 4*91 + 6*72 + 3*91 + 5*78 + 12*70 + 3*89 + 6*76 + 2*94 = 7,936$ 6. Number of data points $n=20$. 7. Substitute into formula: $$r = \frac{20 \times 7936 - 116 \times 1441}{\sqrt{(20 \times 812 - 116^2)(20 \times 105927 - 1441^2)}}$$ Calculate numerator: $20 \times 7936 = 158,720$ $116 \times 1441 = 167,156$ Numerator = 158,720 - 167,156 = -8,436$ Calculate denominator: $20 \times 812 = 16,240$ $116^2 = 13,456$ $20 \times 105,927 = 2,118,540$ $1441^2 = 2,076,481$ Denominator = $\sqrt{(16,240 - 13,456)(2,118,540 - 2,076,481)} = \sqrt{2,784 \times 42,059} = \sqrt{117,086,256} \approx 10,823.9$ 8. Therefore, $$r = \frac{-8,436}{10,823.9} \approx -0.78$$ 9. Interpretation: There is a strong negative correlation ($r \approx -0.78$) between days missed and semester grade, meaning as days missed increase, semester grade tends to decrease. Final answer: The correlation coefficient between days missed and semester grade is approximately $-0.78$, indicating a strong negative relationship.