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Scatter Plots

Grade 8 · Statistics · Worksheet 2

  1. Liam is studying the relationship between study time and test scores. He collected data from 8 classmates and created a scatter plot showing study time (hours) on the x-axis and test scores (percentage) on the y-axis. The scatter plot shows a positive linear association with a line of best fit equation: y = 5x + 65. If Noah studied for 3.5 hours, what test score would the line of best fit predict for him? Answer: ______________
  2. Mere is investigating the relationship between the number of hours spent on social media per week and the number of books read per month among her classmates. She surveys 12 students and records their data. She creates a scatter plot with hours on social media on the x-axis and books read on the y-axis. The data shows a negative linear association. Mere draws a line of best fit that passes through the points (2, 8) and (10, 4). Based on this trend, how many books per month would you predict for a student who spends 6 hours per week on social media? Answer: ______________
  3. Emma records the number of pages read (x) and the time in minutes (y) for five books: (10, 15), (20, 30), (30, 45), (40, 60), (50, 75). Describe the association shown by the scatter plot. Answer: ______________
  4. Isabella records the number of hours studied (x) and the test score (y) for 8 students: (8, 72), (10, 78), (12, 84), (14, 86), (16, 90), (18, 92), (20, 94), (22, 96). Describe the association between hours studied and test score. Answer: ______________
  5. Liam recorded the number of pages he read each day and the time (in minutes) he spent reading over a week. He collected the following data points: (10, 15), (15, 20), (20, 30), (25, 35), (30, 45), (35, 50), (40, 60), where x is pages read and y is minutes spent. If the line of best fit for this data is y = 1.5x + 0, what would be the predicted minutes spent reading for a day when Liam reads 50 pages? Answer: ______________
  6. Matiu records the number of hours studied and the test scores for 8 students: (2, 55), (4, 65), (6, 72), (8, 78), (10, 82), (12, 87), (14, 90), (16, 94). Construct a scatter plot of this data and describe the type of association (positive, negative, or no correlation) and the strength (strong, moderate, or weak). Answer: ______________
  7. √(81) + 5² - 2³ = ? Answer: ______________
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Answer Key & Explanations

Scatter Plots · Grade 8 · Worksheet 2

  1. Liam is studying the relationship between study time and test scores. He collected data from 8 classmates and created a scatter plot showing study time (hours) on the x-axis and test scores (percentage) on the y-axis. The scatter plot shows a positive linear association with a line of best fit equation: y = 5x + 65. If Noah studied for 3.5 hours, what test score would the line of best fit predict for him? Answer: 82.5 Solution: y = 5x + 65 - y = predicted test score (percentage) - x = study time (hours) Noah studied for 3.5 hours, so x = 3.5. Substitute x = 3.5 into the equation. y = 5 * (3.5) + 65 Multiply 5 by 3.5.
    Full step-by-step solution

    We are given the line of best fit equation: y = 5x + 65 Here: - y = predicted test score (percentage) - x = study time (hours) Noah studied for 3.5 hours, so x = 3.5. Step 1: Substitute x = 3.5 into the equation. y = 5 * (3.5) + 65 Step 2: Multiply 5 by 3.5. 5 * 3.5 = 17.5 Step 3: Add 65 to the result from Step 2. y = 17.5 + 65 Step 4: Perform the addition. 17.5 + 65 = 82.5 So, the line of best fit predicts Noah’s test score to be 82.5. Final answer: 82.5

  2. Mere is investigating the relationship between the number of hours spent on social media per week and the number of books read per month among her classmates. She surveys 12 students and records their data. She creates a scatter plot with hours on social media on the x-axis and books read on the y-axis. The data shows a negative linear association. Mere draws a line of best fit that passes through the points (2, 8) and (10, 4). Based on this trend, how many books per month would you predict for a student who spends 6 hours per week on social media? Answer: 6 Solution: Find the slope of the line of best fit using the two points (2, 8) and (10, 4). Slope = (y2 - y1) / (x2 - x1) = (4 - 8) / (10 - 2) = (-4) / 8 = -0.5 Use point-slope form with one of the points to find the equation.
    Full step-by-step solution

    Step 1: Find the slope of the line of best fit using the two points (2, 8) and (10, 4). Slope = (y2 - y1) / (x2 - x1) = (4 - 8) / (10 - 2) = (-4) / 8 = -0.5 Step 2: Use point-slope form with one of the points to find the equation. Using (2, 8): y - 8 = -0.5(x - 2) Step 3: Simplify to slope-intercept form. y - 8 = -0.5x + 1 y = -0.5x + 9 Step 4: Substitute x = 6 (hours on social media) into the equation. y = -0.5(6) + 9 y = -3 + 9 y = 6 The predicted number of books read per month for 6 hours of social media is 6 books. The answer is 6.

  3. Emma records the number of pages read (x) and the time in minutes (y) for five books: (10, 15), (20, 30), (30, 45), (40, 60), (50, 75). Describe the association shown by the scatter plot. Answer: Strong positive linear association Solution: List the ordered pairs: (10,15), (20,30), (30,45), (40,60), (50,75). Notice that as x increases by 10, y increases by 15 each time. The points all lie exactly on a straight line (y = 1.5x).
    Full step-by-step solution

    Step 1: List the ordered pairs: (10,15), (20,30), (30,45), (40,60), (50,75). Step 2: Notice that as x increases by 10, y increases by 15 each time. Step 3: The points all lie exactly on a straight line (y = 1.5x). Step 4: Since both variables increase together and the points form a perfect line, the association is strong, positive, and linear. The answer is strong positive linear association.

  4. Isabella records the number of hours studied (x) and the test score (y) for 8 students: (8, 72), (10, 78), (12, 84), (14, 86), (16, 90), (18, 92), (20, 94), (22, 96). Describe the association between hours studied and test score. Answer: Strong positive linear association Solution: List the ordered pairs: (8,72), (10,78), (12,84), (14,86), (16,90), (18,92), (20,94), (22,96). Observe the x-values (hours studied) increase from 8 to 22.
    Full step-by-step solution

    Step 1: List the ordered pairs: (8,72), (10,78), (12,84), (14,86), (16,90), (18,92), (20,94), (22,96). Step 2: Observe the x-values (hours studied) increase from 8 to 22. Step 3: Observe the y-values (test scores) increase from 72 to 96 as x increases. Step 4: Since both variables increase together, the association is positive. Step 5: The points are very close to forming a straight line (the increase is fairly consistent), so the association is strong and linear. Conclusion: The scatter plot shows a strong positive linear association between hours studied and test score.

  5. Liam recorded the number of pages he read each day and the time (in minutes) he spent reading over a week. He collected the following data points: (10, 15), (15, 20), (20, 30), (25, 35), (30, 45), (35, 50), (40, 60), where x is pages read and y is minutes spent. If the line of best fit for this data is y = 1.5x + 0, what would be the predicted minutes spent reading for a day when Liam reads 50 pages? Answer: 75 Solution: Identify the line of best fit equation: y = 1.5x + 0, where x is the number of pages read and y is the time in minutes. Step 2: Substitute x = 50 into the equation: y = 1.5 * 50 + 0. Step 3: Multiply: 1.5 * 50 = 75.
    Full step-by-step solution

    Step 1: Identify the line of best fit equation: y = 1.5x + 0, where x is the number of pages read and y is the time in minutes. Step 2: Substitute x = 50 into the equation: y = 1.5 * 50 + 0. Step 3: Multiply: 1.5 * 50 = 75. Step 4: Add: 75 + 0 = 75. The predicted time is 75 minutes.

  6. Matiu records the number of hours studied and the test scores for 8 students: (2, 55), (4, 65), (6, 72), (8, 78), (10, 82), (12, 87), (14, 90), (16, 94). Construct a scatter plot of this data and describe the type of association (positive, negative, or no correlation) and the strength (strong, moderate, or weak). Answer: Positive, strong association Solution: Plot each pair of values on a coordinate grid with hours studied on the x-axis and test scores on the y-axis. Observe the pattern: as x increases from 2 to 16, y increases from 55 to 94.
    Full step-by-step solution

    Step 1: Plot each pair of values on a coordinate grid with hours studied on the x-axis and test scores on the y-axis. Step 2: Observe the pattern: as x increases from 2 to 16, y increases from 55 to 94. This shows a positive association (both variables increase together). Step 3: Check how closely the points follow a straight line. The points are (2,55), (4,65), (6,72), (8,78), (10,82), (12,87), (14,90), (16,94). They rise steadily and are very close to a straight line, with only small deviations. Step 4: Because the points cluster tightly around an upward-sloping line, the association is strong. The answer is: positive, strong association.

  7. √(81) + 5² - 2³ = ? Answer: 26 Solution: Evaluate the square root: √(81) = 9 Evaluate the exponent: 5² = 25 Evaluate the other exponent: 2³ = 8 Substitute back into the expression: 9 + 25 - 8 Perform addition: 9 + 25 = 34 Perform subtraction: 34 - 8 = 26 The answer is 26.
    Full step-by-step solution

    Step 1: Evaluate the square root: √(81) = 9 Step 2: Evaluate the exponent: 5² = 25 Step 3: Evaluate the other exponent: 2³ = 8 Step 4: Substitute back into the expression: 9 + 25 - 8 Step 5: Perform addition: 9 + 25 = 34 Step 6: Perform subtraction: 34 - 8 = 26 The answer is 26.