Word Problems
Overview
Apply your data analysis skills to real-world scenarios. These word problems require you to interpret scatter plots, use lines of best fit to make predictions, and understand correlations in context.
Practice Problems
Question 1: A store tracks advertising spending (in hundreds of dollars) vs. weekly sales (in thousands). The line of best fit is y = 1.2x + 15. If they spend $800 on advertising, predict weekly sales.
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Answer: $24,600 in weekly sales
x = 8 (hundreds of dollars). y = 1.2(8) + 15 = 9.6 + 15 = 24.6 thousand dollars = $24,600.
Question 2: Scientists measure temperature (F) vs. cricket chirps per minute. Data shows positive correlation with equation y = 4x - 160. At 75F, how many chirps per minute are predicted?
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Answer: 140 chirps per minute
y = 4(75) - 160 = 300 - 160 = 140 chirps per minute.
Question 3: A car's value decreases over time. The line of best fit is V = -2500t + 30000, where V is value in dollars and t is years. What does the slope -2500 mean in context?
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Answer: The car loses $2,500 in value each year
The slope represents the rate of change - here, the car depreciates by $2,500 annually.
Question 4: Data shows ice cream sales vs. drowning incidents have a strong positive correlation. Can we conclude ice cream causes drowning?
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Answer: No - correlation does not imply causation
Both variables are likely affected by a third factor (hot weather). Correlation shows relationship, not cause.
Question 5: A fitness tracker shows steps walked (thousands) vs. calories burned with equation y = 50x + 200. What does the y-intercept 200 represent?
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Answer: Baseline calories burned (200) without walking
Even with 0 steps, the body burns about 200 calories from basic metabolic processes tracked in this period.
Question 6: Student height vs. math scores shows no correlation (r close to 0). What does this tell us?
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Answer: Height and math scores have no linear relationship
A student's height does not predict their math performance - the variables are independent.
Question 7: A company's profit model is P = 3.5x - 500, where x is units sold. How many units must be sold to break even (P = 0)?
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Answer: Approximately 143 units
0 = 3.5x - 500; 500 = 3.5x; x = 500/3.5 = 142.86, round up to 143 units.
Question 8: Plant growth data shows height = 2.1(weeks) + 3.5 cm. A plant after 6 weeks is actually 18 cm. Calculate the residual.
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Answer: Residual = 1.9 cm
Predicted: 2.1(6) + 3.5 = 16.1 cm. Residual = Actual - Predicted = 18 - 16.1 = 1.9 cm (above the line).
Question 9: Movie length (minutes) vs. ticket price shows weak negative correlation. Write one sentence interpreting this.
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Answer: Longer movies tend to have slightly lower ticket prices, but the relationship is weak.
The weak correlation means many other factors (genre, theater, time) affect price more than length.
Question 10: Using the equation y = 0.85x + 12, where x is hours practiced and y is performance score, is it reasonable to predict the score for x = 100 hours if the data only covered 0-20 hours?
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Answer: No - extrapolating far beyond the data range is unreliable
The linear relationship may not hold at extreme values. Predictions should stay within or close to the original data range.