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Scatter Plots

Grade 8 · Statistics · Worksheet 2

  1. 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: ______________
  2. Emma is analyzing the relationship between hours spent practicing piano each week and scores on a music performance assessment. She collected data from 12 students and created a scatter plot with practice hours on the x-axis and performance scores (out of 100) on the y-axis. The scatter plot shows a strong positive linear association. Emma calculates the line of best fit as y = 3.2x + 72. Based on this trend, what performance score would you predict for a student who practices 6 hours per week? Answer: ______________
  3. Aroha collected data on the ages (in years) and the number of books read in a year for 12 students in her class. She recorded the following pairs: (11, 9), (12, 12), (13, 14), (14, 18), (15, 22), (16, 25), (17, 30), (18, 35), (19, 38), (20, 42), (21, 45), (22, 50). She plots these points on a scatter plot with age on the x-axis and number of books read on the y-axis. Describe the association between age and number of books read, and explain what the pattern suggests. Answer: ______________
  4. Isabella is a Grade 8 student investigating whether there is a relationship between the number of hours students spend on homework per week and their scores on a science quiz. She collected data from 10 classmates and organized it into the following ordered pairs, where x = hours of homework and y = quiz score (out of 100): (2, 57), (4, 62), (5, 67), (5, 72), (7, 77), (7, 82), (8, 87), (10, 92), (11, 97), (12, 102). After plotting these points on a scatter plot, Isabella sees that the data points form a strong linear pattern. What type of association does the scatter plot show, and what does that mean in the context of this investigation? Answer: ______________
  5. Sophia is a Grade 8 student studying the relationship between the number of hours spent watching educational videos per week and science quiz scores. She surveys 11 classmates and records their hours (x) and scores out of 100 (y). The scatter plot shows a positive linear association. Sophia draws a line of best fit that passes through the points (1, 61) and (6, 86). Based on this trend, what science quiz score would the line predict for a student who watches 4 hours of educational videos per week? Answer: ______________
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Answer Key & Explanations

Scatter Plots · Grade 8 · Worksheet 2

  1. 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.

  2. Emma is analyzing the relationship between hours spent practicing piano each week and scores on a music performance assessment. She collected data from 12 students and created a scatter plot with practice hours on the x-axis and performance scores (out of 100) on the y-axis. The scatter plot shows a strong positive linear association. Emma calculates the line of best fit as y = 3.2x + 72. Based on this trend, what performance score would you predict for a student who practices 6 hours per week? Answer: 91.2 Solution: The line of best fit equation is y = 3.2x + 72, where x represents practice hours and y represents performance score.
    Full step-by-step solution

    Step 1: The line of best fit equation is y = 3.2x + 72, where x represents practice hours and y represents performance score. Step 2: Substitute x = 6 (hours practiced) into the equation: y = 3.2(6) + 72 Step 3: Multiply 3.2 × 6 = 19.2 Step 4: Add 19.2 + 72 = 91.2 Step 5: The predicted performance score is 91.2 out of 100.

  3. Aroha collected data on the ages (in years) and the number of books read in a year for 12 students in her class. She recorded the following pairs: (11, 9), (12, 12), (13, 14), (14, 18), (15, 22), (16, 25), (17, 30), (18, 35), (19, 38), (20, 42), (21, 45), (22, 50). She plots these points on a scatter plot with age on the x-axis and number of books read on the y-axis. Describe the association between age and number of books read, and explain what the pattern suggests. Answer: There is a strong positive association between age and number of books read; as age increases, the number of books read generally increases in a roughly linear pattern. Solution: Look at the ordered pairs: as age increases from 11 to 22, the number of books read increases from 9 to 50.
    Full step-by-step solution

    Step 1: Look at the ordered pairs: as age increases from 11 to 22, the number of books read increases from 9 to 50. Step 2: Notice the trend: each time age increases by 1 year, the number of books read increases by a varying amount, but always upward. For example, from (11,9) to (12,12) is +3 books; from (12,12) to (13,14) is +2; from (13,14) to (14,18) is +4; overall the increases are positive. Step 3: The points are close to forming a straight line (they climb steadily from left to right). Step 4: This means there is a strong positive linear association: as one variable (age) increases, the other variable (books read) also increases. Step 5: The pattern suggests that older students tend to read more books per year, possibly due to improved reading skills or more reading assignments. The answer is: There is a strong positive association between age and number of books read; as age increases, the number of books read generally increases in a roughly linear pattern.

  4. Isabella is a Grade 8 student investigating whether there is a relationship between the number of hours students spend on homework per week and their scores on a science quiz. She collected data from 10 classmates and organized it into the following ordered pairs, where x = hours of homework and y = quiz score (out of 100): (2, 57), (4, 62), (5, 67), (5, 72), (7, 77), (7, 82), (8, 87), (10, 92), (11, 97), (12, 102). After plotting these points on a scatter plot, Isabella sees that the data points form a strong linear pattern. What type of association does the scatter plot show, and what does that mean in the context of this investigation? Answer: The scatter plot shows a strong positive linear association, meaning that as the number of hours spent on homework increases, the science quiz scores also tend to increase. Solution: List the ordered pairs: (2, 57), (4, 62), (5, 67), (5, 72), (7, 77), (7, 82), (8, 87), (10, 92), (11, 97), (12, 102). Step 2: Observe the trend in the y-values as the x-values increase.
    Full step-by-step solution

    Step 1: List the ordered pairs: (2, 57), (4, 62), (5, 67), (5, 72), (7, 77), (7, 82), (8, 87), (10, 92), (11, 97), (12, 102). Step 2: Observe the trend in the y-values as the x-values increase. For example, when x = 2, y = 57; when x = 4, y = 62; when x = 5, y = 67 and 72; when x = 7, y = 77 and 82; when x = 8, y = 87; when x = 10, y = 92; when x = 11, y = 97; when x = 12, y = 102. The y-values consistently increase as x increases. Step 3: Since both variables increase together, this indicates a positive association. Step 4: The points lie close to a straight line (e.g., from (2,57) to (12,102), the y-values increase by about 5 for every increase of 1 in x), showing a strong linear relationship. Step 5: In context, this means students who spend more hours on homework tend to get higher science quiz scores. The answer is: The scatter plot shows a strong positive linear association, meaning that as homework hours increase, quiz scores tend to increase.

  5. Sophia is a Grade 8 student studying the relationship between the number of hours spent watching educational videos per week and science quiz scores. She surveys 11 classmates and records their hours (x) and scores out of 100 (y). The scatter plot shows a positive linear association. Sophia draws a line of best fit that passes through the points (1, 61) and (6, 86). Based on this trend, what science quiz score would the line predict for a student who watches 4 hours of educational videos per week? Answer: 76 Solution: Find the slope of the line of best fit using the points (1, 61) and (6, 86). Slope = (86 - 61) / (6 - 1) = 25 / 5 = 5. Use the slope-intercept form y = mx + b.
    Full step-by-step solution

    Step 1: Find the slope of the line of best fit using the points (1, 61) and (6, 86). Slope = (86 - 61) / (6 - 1) = 25 / 5 = 5. Step 2: Use the slope-intercept form y = mx + b. Substitute one point, say (1, 61), and slope m = 5: 61 = 5(1) + b => 61 = 5 + b => b = 56. Step 3: The equation of the line is y = 5x + 56. Step 4: Substitute x = 4 into the equation: y = 5(4) + 56 = 20 + 56 = 76. The predicted score for 4 hours of videos is 76.