Scatter Plots

lessonbunny.com

Answer Key & Explanations

Scatter Plots · Grade 8 · Worksheet 1

1. Noah is studying the relationship between the number of pages in a book and the time it takes him to read it. He records data for 10 books: (120, 4), (150, 5), (200, 7), (250, 8), (300, 10), (350, 12), (400, 13), (450, 15), (500, 17), (550, 18), where x is the number of pages and y is the reading time in hours. He creates a scatter plot of the data. Describe the association between the number of pages and reading time shown by the scatter plot. What does this association suggest? Answer: The scatter plot shows a strong positive linear association, suggesting that as the number of pages increases, the reading time also increases at a roughly constant rate. Solution: Look at the ordered pairs: (120,4), (150,5), (200,7), (250,8), (300,10), (350,12), (400,13), (450,15), (500,17), (550,18). As x (pages) increases from 120 to 550, y (hours) increases from 4 to 18.
   Full step-by-step solution

   Step 1: Look at the ordered pairs: (120,4), (150,5), (200,7), (250,8), (300,10), (350,12), (400,13), (450,15), (500,17), (550,18). Step 2: As x (pages) increases from 120 to 550, y (hours) increases from 4 to 18. Both variables increase together, so the association is positive. Step 3: The points roughly follow a straight line (the increases are fairly consistent: every 50 pages adds about 1.5 to 2 hours), so the association is linear. Step 4: The points are close to a line, so the association is strong. Step 5: Conclusion: There is a strong positive linear association between pages and reading time. This suggests that books with more pages generally take longer to read, and the relationship is predictable and consistent. The answer is: The scatter plot shows a strong positive linear association, suggesting that as the number of pages increases, the reading time also increases at a roughly constant rate.

2. (6.3 × 10⁵) ÷ (9.0 × 10²) = ? Answer: 700 Solution: Divide the coefficients: 6.3 ÷ 9.0 = 0.7 Subtract the exponents: 5 - 2 = 3 Combine the results: 0.7 × 10³ Convert to standard form: 0.7 × 1000 = 700 The answer is 700.
   Full step-by-step solution

   Step 1: Divide the coefficients: 6.3 ÷ 9.0 = 0.7 Step 2: Subtract the exponents: 5 - 2 = 3 Step 3: Combine the results: 0.7 × 10³ Step 4: Convert to standard form: 0.7 × 1000 = 700 The answer is 700.

3. 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

4. Hana records the number of hours studied (x) and the test score (y) for 8 students: (2, 64), (4, 72), (6, 80), (8, 88), (10, 96), (12, 100), (14, 98), (16, 94). Construct a scatter plot of this bivariate data and describe the association (form, direction, strength, and any outliers). Answer: The scatter plot shows a curved (non-linear) association that is positive for lower x-values, then becomes negative for higher x-values; the relationship is strong; there are no clear outliers. Solution: Draw a coordinate plane with x-axis labeled 'Hours Studied' (from 0 to 18) and y-axis labeled 'Test Score' (from 60 to 100). Step 2: Plot each point: (2,64), (4,72), (6,80), (8,88), (10,96), (12,100), (14,98), (16,94).
   Full step-by-step solution

   Step 1: Draw a coordinate plane with x-axis labeled 'Hours Studied' (from 0 to 18) and y-axis labeled 'Test Score' (from 60 to 100). Step 2: Plot each point: (2,64), (4,72), (6,80), (8,88), (10,96), (12,100), (14,98), (16,94). Step 3: Observe the pattern: from 2 to 12 hours, scores increase steadily (positive association). After 12 hours, scores decrease slightly (negative association). The points form a curve that rises then falls, so the form is non-linear (curved). The direction is positive then negative. The points are very close to the curve, so the association is strong. No point is far from the pattern, so there are no outliers. Final description: curved (non-linear) association, positive then negative, strong, no outliers.

5. Noah records the number of pages read (x) and the time in minutes (y) for 6 students: (11, 16), (21, 26), (31, 36), (41, 46), (51, 56), (61, 66). Describe the association shown by the scatter plot of this data. Answer: strong positive linear association Solution: List the ordered pairs: (11,16), (21,26), (31,36), (41,46), (51,56), (61,66). Notice that as x increases by 10 each time, y also increases by 10 each time.
   Full step-by-step solution

   Step 1: List the ordered pairs: (11,16), (21,26), (31,36), (41,46), (51,56), (61,66). Step 2: Notice that as x increases by 10 each time, y also increases by 10 each time. Step 3: This means the points fall exactly on a straight line with a positive slope. Step 4: Since all points lie perfectly on a line and both variables increase together, the association is strong, positive, and linear. The answer is: strong positive linear association.

6. A scatter plot shows the relationship between daily screen time (hours) and math test scores (percentage) for 25 eighth-grade students. The data points form a pattern that slopes downward from left to right, with most points clustered around an imaginary line. The line of best fit passes through points (1, 92) and (6, 67). What is the slope of this line of best fit? Answer: -5 Solution: Identify the coordinates of the two points: (1, 92) and (6, 67) Calculate the change in y-values (vertical change): 67 - 92 = -25 Calculate the change in x-values (horizontal change): 6 - 1 = 5 Calculate the slope using the formula: slope = (change in y)/(change in x) = -25/5 Simplify the…
   Full step-by-step solution

   Step 1: Identify the coordinates of the two points: (1, 92) and (6, 67) Step 2: Calculate the change in y-values (vertical change): 67 - 92 = -25 Step 3: Calculate the change in x-values (horizontal change): 6 - 1 = 5 Step 4: Calculate the slope using the formula: slope = (change in y)/(change in x) = -25/5 Step 5: Simplify the fraction: -25 ÷ 5 = -5 The answer is -5.

7. (4.2 × 10⁵) ÷ (7.0 × 10²) = ? Answer: 600 Solution: Divide the coefficients: 4.2 ÷ 7.0 = 0.6 Subtract the exponents: 5 - 2 = 3 Combine the results: 0.6 × 10³ Convert to standard form: 0.6 × 1000 = 600 The answer is 600.
   Full step-by-step solution

   Step 1: Divide the coefficients: 4.2 ÷ 7.0 = 0.6 Step 2: Subtract the exponents: 5 - 2 = 3 Step 3: Combine the results: 0.6 × 10³ Step 4: Convert to standard form: 0.6 × 1000 = 600 The answer is 600.