A class measures pencil lengths to the nearest 1/4 inch and gets these values: 5, 5 1/4, 5 1/4, 5 1/2, 5 3/4, 6. On a line plot, how many X's are stacked above 5 1/4?
A1
B2
C3
D4
On a line plot, you place one X above a value for each time that value appears in the data. The value 5 1/4 appears exactly twice in the data set, so 2 X's are stacked above that position. Taller stacks show more frequent values — that visual feature lets you identify the mode at a glance.
Question 2 Multiple Choice
A student records daily temperatures for one week (Monday through Sunday), plots one dot for each day, then connects all the dots with a line. What type of display has this student accidentally created?
AA line plot — connecting the dots is the correct way to complete the display
BA bar graph — the dots and connecting line together act as bars
CA line graph — which shows change over time, not the distribution of a measurement set
DA pictograph — each dot represents one data point symbolically
When points are placed for each day and connected in sequence, the result is a LINE GRAPH, which shows how something changes over time. A line plot never connects the X's — doing so would imply a time trend that isn't there. The two displays are easy to confuse by name: line plots show the distribution of a single measurement set; line graphs show change over time.
Question 3 True / False
On a line plot, stacks with more X's indicate values that appear more frequently in the data.
TTrue
FFalse
Answer: True
This is the fundamental reading principle of a line plot. Each X represents one data point. When multiple data points share the same value, X's stack vertically above that position on the number line. Taller stacks mean more frequent values — you can identify the mode (most common value) instantly by finding the tallest stack.
Question 4 True / False
A line plot and a line graph display the same kind of information and can be used interchangeably.
TTrue
FFalse
Answer: False
These are fundamentally different displays. A LINE PLOT shows the distribution of a set of values — it has no time axis and the X's are never connected. A LINE GRAPH shows how a value changes over time — the points are connected to reveal a trend. Confusing them is one of the most common errors in data analysis. Always check: am I showing the spread of a collection of measurements (line plot) or change over time (line graph)?
Question 5 Short Answer
When creating a line plot for measurements taken to the nearest 1/4 inch, why must the number line include every 1/4-inch interval, even ones where no data appears?
Think about your answer, then reveal below.
Model answer: The number line must show every equal interval between the minimum and maximum values because spacing represents actual numerical distance. Skipping intervals with no data would make the gaps between values look equal when they are not, distorting the shape of the distribution. A value of 5 and 5 1/2 need a visible 5 1/4 gap between them even if nothing was measured at 5 1/4. Equal spacing ensures the plot accurately represents the data.
Even spacing is what makes a line plot an accurate representation rather than a misleading one. If you only mark positions where data exists, you lose the ability to see the true spread and clustering of values. In fractional line plots especially, the equal spacing at every 1/4 unit connects the display to students' understanding of fractions as equally-spaced points on a number line.