1. **Problem statement:** We have 14 students' scores for Chemistry (independent variable, x) and ITGS (dependent variable, y). We need to plot the points, describe their correlation, find mean scores, plot the mean point, draw and find the line of best fit, then estimate ITGS score for Chemistry score 50%. 2. **Plot the points and describe the correlation:** The points are (45,42), (67,76), (72,59), (34,44), (88,76), (91,88), (56,55), (39,45), (77,69), (59,62), (66,58), (82,94), (96,85), (42,58). Plotting these on a scatter plot with Chemistry scores on x-axis and ITGS scores on y-axis shows a general positive trend where higher Chemistry scores tend to correspond to higher ITGS scores, suggesting a positive correlation. 3. **Calculate mean scores:** Mean Chemistry score $$= \frac{45 + 67 + 72 + 34 + 88 + 91 + 56 + 39 + 77 + 59 + 66 + 82 + 96 + 42}{14}$$ $$= \frac{912}{14} = 65.14$$ (approx) Mean ITGS score $$= \frac{42 + 76 + 59 + 44 + 76 + 88 + 55 + 45 + 69 + 62 + 58 + 94 + 85 + 58}{14}$$ $$= \frac{911}{14} = 65.07$$ (approx) 4. **Plot mean point and line of best fit:** The mean point is approximately $$(65.14, 65.07)$$ which we plot on the diagram. By eye, the line of best fit approximates a positive slope, passing near the mean point and capturing the trend of the points. 5. **Find equation of the line of best fit using y-intercept and mean point:** Assume line: $$y = mx + c$$ From the scatter plot or estimation, approximate y-intercept $$c \approx 20$$ (a reasonable guess from the lowest extrapolated y-value). Using mean point $$(65.14, 65.07)$$: $$65.07 = m \times 65.14 + 20$$ $$m = \frac{65.07 - 20}{65.14} = \frac{45.07}{65.14} \approx 0.692$$ Equation of line of best fit: $$y = 0.692x + 20$$ 6. **Estimate ITGS score when Chemistry score is 50%:** Substitute $$x=50$$ in the equation: $$y = 0.692 \times 50 + 20 = 34.6 + 20 = 54.6$$ Estimated ITGS score is approximately 55% when Chemistry score is 50%. Final answers: - Mean Chemistry score: 65.14 - Mean ITGS score: 65.07 - Line of best fit: $$y = 0.692x + 20$$ - Estimated ITGS score for Chemistry 50%: 55