Line Plots — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A line plot shows marble weights in ounces: 14→3 Xs, 12→4 Xs, 34→5 Xs, 1→2 Xs. A student says the median weight is 34 ounce because it has the most X marks.
Corrected: Having the most X marks gives the mode, not the median. The mode is 34 ounce. To find the median, list all 14 values in order and find the middle value.
The value with the most X marks is the mode, not the median. The median requires listing all 14 data points in order and finding the middle value, which is a completely different process.
2. Fix the sentence:
A line plot shows bead sizes in centimeters: 18→6 Xs, 28→3 Xs, 38→2 Xs, 48→5 Xs. A student says the total number of beads is 4 because there are 4 sizes shown.
Corrected: The total number of beads is 16 (6 + 3 + 2 + 5 = 16). There are 4 sizes shown, but each X mark represents one bead.
The 4 sizes on the number line are categories, not data points. Each X mark represents one bead, so you add all X marks: 6 + 3 + 2 + 5 = 16 beads total.
3. Fix the sentence:
A line plot shows liquid in bottles (liters): 14→2 Xs, 12→7 Xs, 34→3 Xs. A student says the least common amount is 14 liter because 14 is the smallest fraction.
Corrected: The least common amount is 14 liter, but the reason is that it has the fewest X marks (2 Xs), not because it is the smallest fraction. The reasoning is about frequency, not size.
The answer happens to be correct, but the reasoning is wrong. The least common amount is determined by which value has the fewest X marks (14 has only 2), not by which fraction is the smallest number.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A line plot shows walking times in hours: 14→6 Xs, 12→3 Xs, 34→5 Xs, 1→1 X. The mode of the data is 14.
The mode is the value that appears most often. Since 14 has 6 X marks, more than any other value (12 has 3, 34 has 5, 1 has 1), it is the mode.
2. Using the walking time data, the number of people who walked 34 hour or longer is 6.
Walking 34 hour or longer includes the values 34 (5 Xs) and 1 (1 X). Adding 5 + 1 = 6 people walked at least 34 hour.
3. A line plot shows fabric lengths in yards: 38→4 Xs, 48→2 Xs, 58→5 Xs, 68→3 Xs. The value that appears the least often is 48.
The value 48 has only 2 X marks, which is fewer than 38 (4 Xs), 58 (5 Xs), or 68 (3 Xs). The least frequent value is the one with the fewest Xs above it.
4. Using the fabric data, how many more pieces measured 58 yard than 38 yard? Answer: 1.
The 58 value has 5 X marks and the 38 value has 4 X marks. The difference is 5 − 4 = 1, so there is 1 more piece at 58 yard than at 38 yard.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A line plot shows rainfall in inches: 18→3 Xs, 28→5 Xs, 38→4 Xs, 48→2 Xs. How many days had more than 28 inch of rain? Explain how you found your answer.
Sample answer: I looked at values greater than 28: 38 has 4 Xs and 48 has 2 Xs. So 4 + 2 = 6 days had more than 28 inch of rain.
A good answer includes: I looked at values greater than 28: 38 has 4 Xs and 48 has 2 Xs. So 4 + 2 = 6 days had more than 28 inch of rain.
2. A line plot shows crayon lengths in inches: 14→4 Xs, 12→3 Xs, 34→5 Xs, 1→2 Xs. What is the total length of all the crayons? Show your work.
Sample answer: Multiply each value by its count and add: (4×14) + (3×12) + (5×34) + (2×1) = 44 + 64 + 154 + 84 = 334 = 814 inches total.
A good answer includes: Multiply each value by its count and add: (4×14) + (3×12) + (5×34) + (2×1) = 44 + 64 + 154 + 84 = 334 = 814 inches total.