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Scatter Plots

Grade 8 · Statistics · Worksheet 3

  1. Mason records the number of hours studied (x) and the test score (y) for 8 students: (2, 62), (4, 72), (6, 77), (8, 82), (10, 87), (12, 92), (14, 97), (16, 102). Describe the association shown in the scatter plot of this data. Answer: ______________
  2. Isabella records the number of pages she reads each day and the time spent reading (in minutes). The data points are: (12, 15), (15, 20), (18, 22), (20, 28), (24, 30), (28, 35), (30, 38), (32, 42). Construct a scatter plot and describe the association between pages read and time spent reading. Answer: ______________
  3. Matiu is studying the relationship between the number of hours students spend reading each week and their scores on a reading comprehension test. He collects data from 10 classmates and creates a scatter plot with reading hours on the x-axis and test scores (out of 100) on the y-axis. The scatter plot shows a positive linear association. Matiu draws a line of best fit that passes through the points (2, 54) and (8, 78). Based on this trend, what reading comprehension score would you predict for a student who reads for 6 hours per week? Answer: ______________
  4. Emma is analyzing the relationship between hours spent practicing basketball and free throw percentage. She collected data from 10 teammates and created a scatter plot with practice hours on the x-axis and free throw percentage on the y-axis. The line of best fit has the equation y = 3.2x + 42. If a player practices for 6 hours per week, what free throw percentage does the line of best fit predict? Answer: ______________
  5. A scatter plot shows the relationship between study time (hours) and test scores (points) for 20 students. The data points form a pattern where as study time increases, test scores generally increase. The line of best fit passes through points (2, 65) and (5, 85). What is the slope of this line of best fit? Answer: ______________
  6. Kaia is studying the relationship between the age of a car (in years) and its resale value (in thousands of dollars). She collected data from 9 used car listings and created a scatter plot with age on the x-axis and resale value on the y-axis. The scatter plot shows a strong negative linear association. Kaia drew a line of best fit that passes through the points (3, 21) and (7, 13). Based on this trend, what resale value (in thousands of dollars) would you predict for a car that is 5 years old? Answer: ______________
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Answer Key & Explanations

Scatter Plots · Grade 8 · Worksheet 3

  1. Mason records the number of hours studied (x) and the test score (y) for 8 students: (2, 62), (4, 72), (6, 77), (8, 82), (10, 87), (12, 92), (14, 97), (16, 102). Describe the association shown in the scatter plot of this data. Answer: strong positive linear association Solution: List the ordered pairs: (2,62), (4,72), (6,77), (8,82), (10,87), (12,92), (14,97), (16,102). As x increases from 2 to 16, y increases from 62 to 102. This shows a positive association.
    Full step-by-step solution

    Step 1: List the ordered pairs: (2,62), (4,72), (6,77), (8,82), (10,87), (12,92), (14,97), (16,102). Step 2: As x increases from 2 to 16, y increases from 62 to 102. This shows a positive association. Step 3: The increase in y is roughly consistent: each time x increases by 2, y increases by about 5 to 10 points. The points nearly lie on a straight line. Step 4: Since the points are close to a line and both variables increase together, the association is strong, positive, and linear. The answer is strong positive linear association.

  2. Isabella records the number of pages she reads each day and the time spent reading (in minutes). The data points are: (12, 15), (15, 20), (18, 22), (20, 28), (24, 30), (28, 35), (30, 38), (32, 42). Construct a scatter plot and describe the association between pages read and time spent reading. Answer: Positive, linear, strong association Solution: Plot each pair on a coordinate grid with pages on the x-axis and time on the y-axis. Points: (12,15), (15,20), (18,22), (20,28), (24,30), (28,35), (30,38), (32,42).
    Full step-by-step solution

    Step 1: Plot each pair on a coordinate grid with pages on the x-axis and time on the y-axis. Step 2: Points: (12,15), (15,20), (18,22), (20,28), (24,30), (28,35), (30,38), (32,42). Step 3: As pages increase from 12 to 32, time increases from 15 to 42. Both variables increase together, so the association is positive. Step 4: The points roughly follow a straight line (e.g., from (12,15) to (32,42) the pattern is consistent), so the association is linear. Step 5: The points are very close to the line (no outliers or wide scatter), so the association is strong. The answer is: Positive, linear, strong association.

  3. Matiu is studying the relationship between the number of hours students spend reading each week and their scores on a reading comprehension test. He collects data from 10 classmates and creates a scatter plot with reading hours on the x-axis and test scores (out of 100) on the y-axis. The scatter plot shows a positive linear association. Matiu draws a line of best fit that passes through the points (2, 54) and (8, 78). Based on this trend, what reading comprehension score would you predict for a student who reads for 6 hours per week? Answer: 70 Solution: Find the slope using the two points (2, 54) and (8, 78). Slope = (78 - 54) / (8 - 2) = 24 / 6 = 4. Use point-slope form with point (2, 54): y - 54 = 4(x - 2).
    Full step-by-step solution

    Step 1: Find the slope using the two points (2, 54) and (8, 78). Slope = (78 - 54) / (8 - 2) = 24 / 6 = 4. Step 2: Use point-slope form with point (2, 54): y - 54 = 4(x - 2). Step 3: Simplify to slope-intercept form: y - 54 = 4x - 8, so y = 4x + 46. Step 4: Substitute x = 6: y = 4(6) + 46 = 24 + 46 = 70. The predicted reading comprehension score for 6 hours of reading per week is 70.

  4. Emma is analyzing the relationship between hours spent practicing basketball and free throw percentage. She collected data from 10 teammates and created a scatter plot with practice hours on the x-axis and free throw percentage on the y-axis. The line of best fit has the equation y = 3.2x + 42. If a player practices for 6 hours per week, what free throw percentage does the line of best fit predict? Answer: 61.2 Solution: Identify the line of best fit equation: y = 3.2x + 42 Substitute x = 6 (practice hours) into the equation: y = 3.2(6) + 42 Multiply: 3.2 × 6 = 19.2 Add: 19.2 + 42 = 61.2 The predicted free throw percentage is 61.2%
    Full step-by-step solution

    Step 1: Identify the line of best fit equation: y = 3.2x + 42 Step 2: Substitute x = 6 (practice hours) into the equation: y = 3.2(6) + 42 Step 3: Multiply: 3.2 × 6 = 19.2 Step 4: Add: 19.2 + 42 = 61.2 Step 5: The predicted free throw percentage is 61.2%

  5. A scatter plot shows the relationship between study time (hours) and test scores (points) for 20 students. The data points form a pattern where as study time increases, test scores generally increase. The line of best fit passes through points (2, 65) and (5, 85). What is the slope of this line of best fit? Answer: 6.67 Solution: Recall the slope formula. The slope of a line through two points (x1, y1) and (x2, y2) is: slope = (y2 - y1) / (x2 - x1) Identify the given points.
    Full step-by-step solution

    Step 1: Recall the slope formula. The slope of a line through two points (x1, y1) and (x2, y2) is: slope = (y2 - y1) / (x2 - x1) Step 2: Identify the given points. Point 1: (2, 65) → x1 = 2, y1 = 65 Point 2: (5, 85) → x2 = 5, y2 = 85 Step 3: Substitute into the slope formula. slope = (85 - 65) / (5 - 2) slope = (20) / (3) Step 4: Calculate the value. 20 / 3 = 6.666... Rounded to two decimal places, this is 6.67. Step 5: Interpret the result. The slope of the line of best fit is 6.67, meaning for each additional hour of study time, the test score increases by about 6.67 points on average. Final Answer: 6.67

  6. Kaia is studying the relationship between the age of a car (in years) and its resale value (in thousands of dollars). She collected data from 9 used car listings and created a scatter plot with age on the x-axis and resale value on the y-axis. The scatter plot shows a strong negative linear association. Kaia drew a line of best fit that passes through the points (3, 21) and (7, 13). Based on this trend, what resale value (in thousands of dollars) would you predict for a car that is 5 years old? Answer: 17 Solution: Find the slope of the line of best fit using the two given points (3, 21) and (7, 13).
    Full step-by-step solution

    Step 1: Find the slope of the line of best fit using the two given points (3, 21) and (7, 13). Slope = (y2 - y1) / (x2 - x1) = (13 - 21) / (7 - 3) = (-8) / 4 = -2 Step 2: Use point-slope form with one of the points to find the equation of the line. Using point (3, 21): y - 21 = -2(x - 3) Step 3: Simplify the equation to slope-intercept form. y - 21 = -2x + 6 y = -2x + 27 Step 4: Substitute x = 5 (the age of the car in years) into the equation. y = -2(5) + 27 y = -10 + 27 y = 17 Step 5: The predicted resale value for a 5-year-old car is 17 thousand dollars. The answer is 17.