Scatter Plots

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Scatter Plots · Grade 8 · Worksheet 1

1. 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.

2. (3.6 × 10⁴) ÷ (1.2 × 10²) = ? Answer: 300 Solution: Separate the coefficients and powers of 10: (3.6 ÷ 1.2) × (10⁴ ÷ 10²) Divide the coefficients: 3.6 ÷ 1.2 = 3 Apply the quotient rule for exponents: 10⁴ ÷ 10² = 10^(4-2) = 10² Multiply the results: 3 × 10² = 3 × 100 = 300 The answer is 300.
   Full step-by-step solution

   Step 1: Separate the coefficients and powers of 10: (3.6 ÷ 1.2) × (10⁴ ÷ 10²) Step 2: Divide the coefficients: 3.6 ÷ 1.2 = 3 Step 3: Apply the quotient rule for exponents: 10⁴ ÷ 10² = 10^(4-2) = 10² Step 4: Multiply the results: 3 × 10² = 3 × 100 = 300 The answer is 300.

3. (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.

4. Aroha records the number of hours studied (x) and the test score out of 100 (y) for 7 students: (1, 55), (3, 65), (5, 75), (7, 85), (9, 95), (11, 105), (13, 115). Plot these points on a scatter plot and describe the type of association (positive, negative, or no correlation) and its strength (strong, moderate, or weak). Answer: Strong positive linear association Solution: Plot the points: (1,55), (3,65), (5,75), (7,85), (9,95), (11,105), (13,115). Step 2: Observe that as x increases, y also increases consistently.
   Full step-by-step solution

   Step 1: Plot the points: (1,55), (3,65), (5,75), (7,85), (9,95), (11,105), (13,115). Step 2: Observe that as x increases, y also increases consistently. Step 3: The points all lie exactly on a straight line (each increase of 2 in x gives an increase of 10 in y). Step 4: This shows a strong positive linear association because the points follow a clear upward trend and are perfectly aligned. The answer is strong positive linear association.

5. Noah is studying the relationship between the number of days students spend practicing a musical instrument each month and their scores on a performance test (out of 100). He collects data from 10 classmates and creates a scatter plot with practice days on the x-axis and test scores on the y-axis. The scatter plot shows a strong positive linear association. Noah draws a line of best fit that passes through the points (4, 55) and (10, 85). Based on this trend, what test score would the line of best fit predict for a student who practices for 7 days in a month? Answer: 70 Solution: Find the slope of the line of best fit using the two given points (4, 55) and (10, 85). Slope = (85 - 55) / (10 - 4) = 30 / 6 = 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 given points (4, 55) and (10, 85). Slope = (85 - 55) / (10 - 4) = 30 / 6 = 5 Step 2: Use point-slope form with one of the points to find the equation. Using point (4, 55): y - 55 = 5(x - 4) Step 3: Simplify to slope-intercept form. y - 55 = 5x - 20 y = 5x + 35 Step 4: Substitute x = 7 (practice days) into the equation. y = 5(7) + 35 y = 35 + 35 y = 70 The predicted test score for 7 days of practice is 70.

6. Liam is studying the relationship between study time and test scores in his math class. 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 data points appear to follow a linear pattern with a positive correlation. Liam calculated the line of best fit as y = 5x + 65. If a student studied for 3.5 hours, what test score would the line of best fit predict? Answer: 82.5 Solution: y = 5x + 65 - x = study time in hours - y = predicted test score in percentage We want the predicted score for a student who studied 3.5 hours, so x = 3.5. Write down the equation with the given x value.
   Full step-by-step solution

   We are given the line of best fit equation: y = 5x + 65 Here: - x = study time in hours - y = predicted test score in percentage We want the predicted score for a student who studied 3.5 hours, so x = 3.5. --- **Step 1: Write down the equation with the given x value.** 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 --- **Step 5: Interpret the result.** The line of best fit predicts a test score of 82.5% for 3.5 hours of study time. **Final answer:** 82.5

7. Plot the points (1, 6), (6, 11), (11, 16), (16, 21). Describe the association shown by the scatter plot. Answer: Positive linear association Solution: Plot the points on a coordinate grid: (1, 6), (6, 11), (11, 16), (16, 21). Observe the pattern: as x increases from 1 to 16, y increases from 6 to 21.
   Full step-by-step solution

   Step 1: Plot the points on a coordinate grid: (1, 6), (6, 11), (11, 16), (16, 21). Step 2: Observe the pattern: as x increases from 1 to 16, y increases from 6 to 21. Step 3: The points all lie on the line y = x + 5, which is a straight line with a positive slope. Step 4: Since the points form a straight line and y increases as x increases, the association is a positive linear association. The answer is positive linear association.