Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Bivariate Patterns

Grade 8 · Statistics · Worksheet 1

  1. (3x - 7)² = 25 Answer: ______________
  2. Mason recorded the number of hours studied (x) and the test score (y) for 8 students: (2, 55), (4, 65), (6, 75), (8, 85), (10, 95), (12, 105), (14, 115), (20, 70). Describe the overall pattern of association and identify any outlier. Answer: ______________
  3. The table shows the number of hours studied and the test scores for eight students. Identify the association pattern and any outliers. Hours studied: 12, 15, 18, 20, 22, 25, 28, 30 Test scores: 55, 62, 68, 75, 80, 85, 92, 50 Answer: ______________
  4. A scatter plot shows the relationship between the number of hours students spend on homework per week and their math test scores. The data points form a linear pattern with a positive association. The line of best fit passes through the points (3, 72) and (7, 88). What is the slope of this line of best fit? Answer: ______________
  5. Emma is analyzing the relationship between the number of practice problems completed and math test scores in her class. She collected data from 7 students and found the line of best fit to be y = 1.8x + 68, where x represents the number of practice problems completed and y represents the test score. According to this model, what test score would be predicted for a student who completes 25 practice problems? Answer: ______________
  6. Emma is analyzing the relationship between the number of practice problems completed and math test scores for students in her class. She collected data and found the line of best fit to be y = 1.8x + 72, where x represents the number of practice problems completed and y represents the test score percentage. According to this model, what test score would be predicted for a student who completes 25 practice problems? Answer: ______________
  7. Liam is analyzing the relationship between study time and test scores in his science class. He collected data from 8 students and created a scatter plot. The line of best fit has the equation y = 2.5x + 65, where x represents study time in hours and y represents test scores. If a student studies for 6 hours, what test score does the model predict? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Bivariate Patterns · Grade 8 · Worksheet 1

  1. (3x - 7)² = 25 Answer: 4 Solution: Start with the equation (3x - 7)² = 25 Take the square root of both sides: 3x - 7 = 5 or 3x - 7 = -5 Solve the first equation: 3x - 7 = 5 → 3x = 12 → x = 4 Solve the second equation: 3x - 7 = -5 → 3x = 2 → x = 2/3 The two solutions are x = 4 and x = 2/3 Since the problem asks for the larger…
    Full step-by-step solution

    Step 1: Start with the equation (3x - 7)² = 25 Step 2: Take the square root of both sides: 3x - 7 = 5 or 3x - 7 = -5 Step 3: Solve the first equation: 3x - 7 = 5 → 3x = 12 → x = 4 Step 4: Solve the second equation: 3x - 7 = -5 → 3x = 2 → x = 2/3 Step 5: The two solutions are x = 4 and x = 2/3 Since the problem asks for the larger solution, the answer is 4.

  2. Mason recorded the number of hours studied (x) and the test score (y) for 8 students: (2, 55), (4, 65), (6, 75), (8, 85), (10, 95), (12, 105), (14, 115), (20, 70). Describe the overall pattern of association and identify any outlier. Answer: Positive association with an outlier at (20, 70) Solution: List the ordered pairs: (2,55), (4,65), (6,75), (8,85), (10,95), (12,105), (14,115), (20,70). Observe the pattern: As hours studied increase from 2 to 14, test scores increase steadily from 55 to 115.
    Full step-by-step solution

    Step 1: List the ordered pairs: (2,55), (4,65), (6,75), (8,85), (10,95), (12,105), (14,115), (20,70). Step 2: Observe the pattern: As hours studied increase from 2 to 14, test scores increase steadily from 55 to 115. This shows a positive association (both variables increase together). Step 3: Check for outliers: The point (20,70) has a high x-value (20 hours studied) but a low y-value (70 test score). Most points with high study hours have high scores (e.g., 14 hours → 115 points). The point (20,70) does not follow the upward trend and is far from the other points. Step 4: Conclusion: The overall pattern is a positive association, and the outlier is (20, 70).

  3. The table shows the number of hours studied and the test scores for eight students. Identify the association pattern and any outliers. Hours studied: 12, 15, 18, 20, 22, 25, 28, 30 Test scores: 55, 62, 68, 75, 80, 85, 92, 50 Answer: Positive association with an outlier at (30, 50) Solution: List the ordered pairs: (12,55), (15,62), (18,68), (20,75), (22,80), (25,85), (28,92), (30,50). Observe the trend: As hours increase from 12 to 28, test scores increase from 55 to 92. This shows a positive association.
    Full step-by-step solution

    Step 1: List the ordered pairs: (12,55), (15,62), (18,68), (20,75), (22,80), (25,85), (28,92), (30,50). Step 2: Observe the trend: As hours increase from 12 to 28, test scores increase from 55 to 92. This shows a positive association. Step 3: Check for outliers: The point (30,50) has a high number of hours (30) but a low test score (50), which does not fit the increasing trend. All other points show scores rising with hours. Step 4: Conclusion: The data has a positive association overall, with an outlier at (30, 50).

  4. A scatter plot shows the relationship between the number of hours students spend on homework per week and their math test scores. The data points form a linear pattern with a positive association. The line of best fit passes through the points (3, 72) and (7, 88). What is the slope of this line of best fit? Answer: 4 Solution: Identify the coordinates of the two points: (3, 72) and (7, 88) Recall the slope formula: slope = (y2 - y1) / (x2 - x1) Substitute the values: slope = (88 - 72) / (7 - 3) Calculate the numerator: 88 - 72 = 16 Calculate the denominator: 7 - 3 = 4 Divide: 16 / 4 = 4 The slope of the line of best…
    Full step-by-step solution

    Step 1: Identify the coordinates of the two points: (3, 72) and (7, 88) Step 2: Recall the slope formula: slope = (y2 - y1) / (x2 - x1) Step 3: Substitute the values: slope = (88 - 72) / (7 - 3) Step 4: Calculate the numerator: 88 - 72 = 16 Step 5: Calculate the denominator: 7 - 3 = 4 Step 6: Divide: 16 / 4 = 4 The slope of the line of best fit is 4.

  5. Emma is analyzing the relationship between the number of practice problems completed and math test scores in her class. She collected data from 7 students and found the line of best fit to be y = 1.8x + 68, where x represents the number of practice problems completed and y represents the test score. According to this model, what test score would be predicted for a student who completes 25 practice problems? Answer: 113 Solution: Identify the given linear equation: y = 1.8x + 68 Substitute x = 25 (the number of practice problems) into the equation: y = 1.8 * 25 + 68 Calculate 1.8 * 25 = 45 Add 68 to the result: 45 + 68 = 113 The predicted test score is 113.
    Full step-by-step solution

    Step 1: Identify the given linear equation: y = 1.8x + 68 Step 2: Substitute x = 25 (the number of practice problems) into the equation: y = 1.8 * 25 + 68 Step 3: Calculate 1.8 * 25 = 45 Step 4: Add 68 to the result: 45 + 68 = 113 Step 5: The predicted test score is 113. The answer is 113.

  6. Emma is analyzing the relationship between the number of practice problems completed and math test scores for students in her class. She collected data and found the line of best fit to be y = 1.8x + 72, where x represents the number of practice problems completed and y represents the test score percentage. According to this model, what test score would be predicted for a student who completes 25 practice problems? Answer: 117 Solution: Identify the given linear equation: y = 1.8x + 72 Substitute x = 25 into the equation: y = 1.8(25) + 72 Multiply 1.8 × 25 = 45 Add 45 + 72 = 117 The predicted test score is 117% The answer is 117.
    Full step-by-step solution

    Step 1: Identify the given linear equation: y = 1.8x + 72 Step 2: Substitute x = 25 into the equation: y = 1.8(25) + 72 Step 3: Multiply 1.8 × 25 = 45 Step 4: Add 45 + 72 = 117 Step 5: The predicted test score is 117% The answer is 117.

  7. Liam is analyzing the relationship between study time and test scores in his science class. He collected data from 8 students and created a scatter plot. The line of best fit has the equation y = 2.5x + 65, where x represents study time in hours and y represents test scores. If a student studies for 6 hours, what test score does the model predict? Answer: 80 Solution: y = 2.5x + 65 - x = study time in hours - y = predicted test score Identify the given value of x. The problem says a student studies for 6 hours, so x = 6. Substitute x = 6 into the equation.
    Full step-by-step solution

    We are given the line of best fit equation: y = 2.5x + 65 Here: - x = study time in hours - y = predicted test score Step 1: Identify the given value of x. The problem says a student studies for 6 hours, so x = 6. Step 2: Substitute x = 6 into the equation. y = 2.5 * 6 + 65 Step 3: Perform the multiplication. 2.5 * 6 = 15 Step 4: Add the result to 65. y = 15 + 65 Step 5: Calculate the final value. y = 80 Step 6: Interpret the result. The model predicts that a student who studies for 6 hours will score 80 on the test. Final answer: 80