Chapter 9 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
Using the graph, calculate the signed change from Tue to Thu.
Read the two measurements: 20 − 18 = 2.
Construct a correctly labeled line graph for daily book checkouts: Mon: 14, Tue: 9, Wed: 4, Thu: 23, Fri: 21. State the highest value.
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Tue to Fri.
Read the two measurements: 20 − 21 = -1.
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 5, Tue: 9, Wed: 12, Thu: 21, Fri: 18. State the highest value.
Choose a consistent axis scale from zero to at least 21; plot all five points in weekday order, connect adjacent points, and identify the maximum of 21.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Thu to Fri.
Read the two measurements: 11 − 11 = 0.
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 11, Tue: 16, Wed: 14, Thu: 21, Fri: 8. State the highest value.
Choose a consistent axis scale from zero to at least 21; plot all five points in weekday order, connect adjacent points, and identify the maximum of 21.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Tue to Thu.
Read the two measurements: 21 − 16 = 5.
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 16, Tue: 4, Wed: 7, Thu: 4, Fri: 17. State the highest value.
Choose a consistent axis scale from zero to at least 17; plot all five points in weekday order, connect adjacent points, and identify the maximum of 17.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Tue to Fri.
Read the two measurements: 12 − 11 = 1.
Construct a correctly labeled line graph for daily book checkouts: Mon: 12, Tue: 13, Wed: 16, Thu: 14, Fri: 8. State the highest value.
Choose a consistent axis scale from zero to at least 16; plot all five points in weekday order, connect adjacent points, and identify the maximum of 16.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Mon to Wed.
Read the two measurements: 12 − 19 = -7.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 22, Tue: 13, Wed: 10, Thu: 20, Fri: 18. State the highest value.
Choose a consistent axis scale from zero to at least 22; plot all five points in weekday order, connect adjacent points, and identify the maximum of 22.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Wed to Fri.
Read the two measurements: 17 − 12 = 5.
Construct a correctly labeled line graph for daily book checkouts: Mon: 7, Tue: 23, Wed: 21, Thu: 6, Fri: 5. State the highest value.
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Wed to Fri.
Read the two measurements: 14 − 16 = -2.
Construct a correctly labeled line graph for daily book checkouts: Mon: 16, Tue: 20, Wed: 8, Thu: 19, Fri: 13. State the highest value.
Choose a consistent axis scale from zero to at least 20; plot all five points in weekday order, connect adjacent points, and identify the maximum of 20.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Using the graph, calculate the signed change from Tue to Fri.
Read the two measurements: 9 − 20 = -11.
Construct a correctly labeled line graph for daily book checkouts: Mon: 14, Tue: 20, Wed: 11, Thu: 23, Fri: 6. State the highest value.
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
A line graph uses a scale marked at 15 and 35. A student assumes halfway between tick marks must mean one more unit. Explain why that method is unreliable.
A point halfway between labeled values must represent their arithmetic mean, not a count of printed tick marks.
A student draws a line graph for daily readings using unequal vertical tick intervals labeled 0, 5, 20, 25. Explain why this can mislead.
The vertical axis must use a consistent numeric scale; unequal steps distort comparisons.
A line plot has three X marks above 2 and four X marks above 5. How many observations does it record?
Each X represents one observation; three plus four gives seven.
A line graph uses a scale marked at 10 and 35. A student assumes halfway between tick marks must mean one more unit. Explain why that method is unreliable.
A point halfway between labeled values must represent their arithmetic mean, not a count of printed tick marks.
Construct a correctly labeled line graph for daily plant height in centimeters: Mon: 11, Tue: 15, Wed: 12, Thu: 13, Fri: 12. State the highest value.
Choose a consistent axis scale from zero to at least 15; plot all five points in weekday order, connect adjacent points, and identify the maximum of 15.
What is the greatest frequency shown on the line plot?
The tallest stack of X marks contains 5 observations.
Practice examination solutions and scoring
From the line graph below, read the number collected on Thu.
Read the plotted point above Thu on the vertical scale: 7.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Fri.
Read the plotted point above Fri on the vertical scale: 22.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is the greatest frequency shown on the line plot?
The tallest stack of X marks contains 4 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 19, Tue: 21, Wed: 4, Thu: 17, Fri: 15. State the highest value.
Choose a consistent axis scale from zero to at least 21; plot all five points in weekday order, connect adjacent points, and identify the maximum of 21.
Scoring (4 points): Award one point each for labeled axes, an even scale, correctly plotted marks/points, and a correct interpretation.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Wed to Thu.
Read the two measurements: 23 − 13 = 10.
Scoring (2 points): Award one point for a sound method and one for the correct result.
On the line plot below, how many observations equal 4?
Count the X marks stacked directly above 4: 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Tue.
Read the plotted point above Tue on the vertical scale: 12.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Thu to Fri.
Read the two measurements: 10 − 11 = -1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Fri.
Read the plotted point above Fri on the vertical scale: 9.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Thu.
Read the plotted point above Thu on the vertical scale: 20.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is the greatest frequency shown on the line plot?
The tallest stack of X marks contains 4 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 14, Tue: 7, Wed: 12, Thu: 9, Fri: 14. State the highest value.
Choose a consistent axis scale from zero to at least 14; plot all five points in weekday order, connect adjacent points, and identify the maximum of 14.
Scoring (4 points): Award one point each for labeled axes, an even scale, correctly plotted marks/points, and a correct interpretation.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Mon to Wed.
Read the two measurements: 18 − 19 = -1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
On the line plot below, how many observations equal 8?
Count the X marks stacked directly above 8: 3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Tue.
Read the plotted point above Tue on the vertical scale: 13.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Mon to Thu.
Read the two measurements: 15 − 14 = 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Wed.
Read the plotted point above Wed on the vertical scale: 18.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Fri.
Read the plotted point above Fri on the vertical scale: 14.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is the greatest frequency shown on the line plot?
The tallest stack of X marks contains 3 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Construct a correctly labeled line graph for daily book checkouts: Mon: 8, Tue: 22, Wed: 23, Thu: 23, Fri: 15. State the highest value.
Choose a consistent axis scale from zero to at least 23; plot all five points in weekday order, connect adjacent points, and identify the maximum of 23.
Scoring (4 points): Award one point each for labeled axes, an even scale, correctly plotted marks/points, and a correct interpretation.
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Thu to Fri.
Read the two measurements: 7 − 11 = -4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
On the line plot below, how many observations equal 6?
Count the X marks stacked directly above 6: 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
From the line graph below, read the number collected on Fri.
Read the plotted point above Fri on the vertical scale: 4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Using the graph, calculate the signed change from Tue to Thu.
Read the two measurements: 12 − 20 = -8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A line graph uses a scale marked at 10 and 45. A student assumes halfway between tick marks must mean one more unit. Explain why that method is unreliable.
A point halfway between labeled values must represent their arithmetic mean, not a count of printed tick marks.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 20, Tue: 9, Wed: 13, Thu: 17, Fri: 7. State the highest value.
Choose a consistent axis scale from zero to at least 20; plot all five points in weekday order, connect adjacent points, and identify the maximum of 20.
Scoring (4 points): Award one point each for labeled axes, an even scale, correctly plotted marks/points, and a correct interpretation.
On the line plot below, how many observations equal 4?
Count the X marks stacked directly above 4: 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A line graph uses a scale marked at 25 and 45. A student assumes halfway between tick marks must mean one more unit. Explain why that method is unreliable.
A point halfway between labeled values must represent their arithmetic mean, not a count of printed tick marks.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
From the line graph below, read the number collected on Thu.
Read the plotted point above Thu on the vertical scale: 10.
Scoring (2 points): Award one point for a sound method and one for the correct result.
How many values in the line plot are greater than 3?
Count the X marks above values larger than 3: 6.
Scoring (2 points): Award one point for a sound method and one for the correct result.