A student measures the lengths of 8 pencils. The 5th pencil is 14 centimeters long. When recording this on a line plot, where should the X mark be placed?
AAbove the number 5, because it is the 5th pencil measured
BAbove the number 14, because 14 cm is the measurement value of that pencil
CAt a height of 14 on the vertical axis, since 14 is the measurement
DAbove the number 8, because there are 8 pencils total
The number-line axis on a line plot shows measurement values, not the order in which data was collected. Every pencil that measures 14 cm gets an X above 14, regardless of when it was measured. Placing the X above 5 (for 'fifth pencil') is the classic confusion — it would make the axis a sequence counter rather than a measurement scale, which destroys the purpose of the graph.
Question 2 Multiple Choice
A class line plot of bean-sprout heights shows 6 X marks stacked above 5 cm and 1 X mark above 9 cm. What does the single X above 9 most likely indicate?
A9 was the first measurement value recorded on the number line
BOnly one sprout in the data set measured 9 cm — an unusually tall measurement compared to the cluster at 5
CThe student counted 9 data points total and placed one X to record the count
D9 is the mode because it has fewer marks, making it less common
Each X on a line plot represents exactly one data point — here, one sprout of that height. A single X above 9 means exactly one sprout measured 9 cm. Compared to the cluster of 6 at 5 cm, this isolated value stands out as unusual. The mode is the value with the MOST X marks (5 cm here, not 9). The total count of all data points is found by adding all the X marks together, not by reading any single position.
Question 3 True / False
On a line plot, the height of the X stack above a value tells you the measurement of the data point at that position.
TTrue
FFalse
Answer: False
The height of the stack (number of X marks) tells you the frequency — how many data points had that measurement. The measurement value itself is the number on the axis below the stack. A stack of 4 X marks above 12 means four objects measured 12 units, not that the measurement is 4. Axis position = measurement value; stack height = count.
Question 4 True / False
The value on a line plot with the tallest stack of X marks is the mode of the data set.
TTrue
FFalse
Answer: True
The mode is the value that appears most often. On a line plot, each X represents one occurrence of that measurement value, so the tallest column shows which value appears most frequently — that is the mode. This is one of the key strengths of line plots: they make the mode visually obvious at a glance without any calculation.
Question 5 Short Answer
A student places X marks above 1, 2, 3, and 4 on her line plot — one X for each object measured, in the order she measured them. The fourth object actually measured 9 cm. Why is this approach wrong?
Think about your answer, then reveal below.
Model answer: The axis of a line plot represents measurement values, not the order objects were measured. The X for the fourth object should be placed above 9 (its measurement in cm), not above 4 (its sequence number). If the student uses sequence numbers instead of measurement values, the plot shows nothing meaningful about the actual data.
A line plot is a display of the distribution of measurements — it answers 'how many objects measured 9 cm?' not 'which object was fourth?' Using the axis as a sequence counter destroys the graph's meaning. After correcting the approach, the line plot will reveal where measurements cluster and how spread out they are, which is the entire point of the display.