Line Plots with Fractions

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🔵Understanding and Reading Line Plots

A line plot (also called a dot plot) is a graph that shows data along a number line. Each X above the number line represents one piece of data.

Key terms:

Mode = most common value (where the most X's are)
Range = largest value minus smallest value
Total = each value multiplied by its count, then all added together

Line plots work with whole numbers AND fractions on the number line.

👀 See a worked example

From the line plot above (ribbon lengths), how many ribbons are shown in total? Count all X's: 2 (at 3 in) + 3 (at 3.5 in) + 2 (at 4 in) + 1 (at 4.5 in) = 8 ribbons.

What is the most common ribbon length? The most X's are above 3.5 inches (3 ribbons). The most common length is 3.5 inches.

How many ribbons are longer than 3.5 inches? At 4 inches: 2 ribbons. At 4.5 inches: 1 ribbon. Total = 3 ribbons longer than 3.5 inches.

🤖 Vidi's Key Points

A line plot shows data using X marks above a number line
Each X represents ONE piece of data
The value with the most X's is the MODE (most common value)
Always count all X's carefully to find the total

🟢Creating Line Plots from Data

How to Create a Line Plot:

Step 1: Find the range — identify the smallest and largest values
Step 2: Draw a number line with equal intervals covering all values
Step 3: Label the number line (use fractions where needed)
Step 4: Place one X above the number for each data point
Step 5: Give the plot a clear title

Line plots with fractions often use intervals of 1/4 or 1/2.

👀 See a worked example

Create a line plot for ribbon lengths (cm): 5, 5.5, 5, 5.5, 6, 5.5, 5, 6 Range: 5 to 6. Draw number line from 5 to 6 with 0.5 intervals. At 5: 3 X's. At 5.5: 3 X's. At 6: 2 X's. Title: Ribbon Lengths (cm).

Data: apple weights (g): 140, 150, 150, 160, 150, 170, 160, 140. Create line plot and find the most common weight. At 140g: 2 X's. At 150g: 3 X's. At 160g: 2 X's. At 170g: 1 X. Most common weight = 150g (most X's).

🤖 Vidi's Key Points

First find the range (min and max values) before drawing
Use equal intervals on the number line — fractions must be equally spaced
Place one X for each data point — do not skip or double-count
Always give the line plot a descriptive title and label the units

🟣Finding Totals and Differences from Line Plots

Line plots help us calculate quickly:

Finding Total: For each value, multiply it by the number of X's above it. Then add all products.

Finding Difference: Subtract the smallest value from the largest value shown on the plot.

Finding Average (Mean): Divide total by the number of data points (number of X's).

These skills apply to line plots with fractions too — multiply fractions by counts carefully!

👀 See a worked example

A line plot shows stick lengths (ft): 2 sticks at 1 ft, 3 sticks at 2 ft, 1 stick at 3 ft. Find total length. Total = (1 x 2) + (2 x 3) + (3 x 1) = 2 + 6 + 3 = 11 feet.

From the same plot, what is the difference between the longest and shortest stick? Longest = 3 ft. Shortest = 1 ft. Difference = 3 - 1 = 2 feet.

Milk in glasses (cups): 1 glass at 1/2 cup, 3 glasses at 3/4 cup, 2 glasses at 1 cup. Total milk? Total = (1/2 x 1) + (3/4 x 3) + (1 x 2) = 1/2 + 9/4 + 2 = 2/4 + 9/4 + 8/4 = 19/4 = 4 3/4 cups.

🤖 Vidi's Key Points

Total = sum of (each value x number of X's at that value)
Difference = largest value minus smallest value on the plot
Mean = Total / number of data points
With fractions: multiply fraction by count carefully, then add all products

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