Lesson 5 of 8 · Grades 3 to 5
Line plots
A line plot puts data on a number line. Each X is one item, so a stack of X marks shows how often a value appears.
Data on a number line
A line plot takes a number line and puts the data on it. Each item in the data becomes one X mark above its value. If two children have the same value, the second X sits on top of the first, and the marks grow into a stack.
Line plots are best for data that is already a number: shoe sizes, goals scored, hours of sleep, the number of pets in a home. The number line shows every value in order, and the stacks show how often each value happens.
Reading a stack
This line plot shows the shoe sizes of the children in class 4. The numbers along the line are the sizes, and each X is one child.
Show the data as a table
| Shoe size | X marks |
|---|---|
| 4 | 1 |
| 5 | 3 |
| 6 | 5 |
| 7 | 2 |
| 8 | 1 |
To read one value, find the number on the line and count the X marks above it. Size 5 has 3 marks, so 3 children have size 5. Size 8 has 1 mark, so 1 child has size 8. The tallest stack is above size 6, which means size 6 is the most common size in the class.
The tallest stack
The value with the most marks is called the mode. On this plot the mode is size 6, because 5 children share it. A line plot shows the mode at a glance: it is simply the tallest stack.
Counting and adding
You can use a line plot to check how many items were collected. Add the heights of the stacks: 1 + 3 + 5 + 2 + 1 = 12, so the class has 12 children. The number of X marks is always the number of items, even when the values are large.
You can also add the values to get a total. The pets line plot below shows how many pets each home has. To find the total number of pets, work out the value of each stack and add the parts: 0 × 1 + 1 × 3 + 2 × 4 + 3 × 2 + 4 × 1 = 0 + 3 + 8 + 6 + 4 = 21 pets.
Show the data as a table
| Number of pets | X marks |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
The plot shows 1 + 3 + 4 + 2 + 1 = 11 homes. Two homes have 3 pets and one home has 4 pets, so 3 homes have at least 3 pets. Every question about the data is answered by reading the stacks and then adding, subtracting or counting.
Building your own line plot
To draw a line plot, write the values along the line from the smallest to the largest, with equal gaps. Then take each item in turn and draw one X above its value, stacking on top of earlier marks. Keep the X marks the same size and shape so the stacks stay easy to count.
Worked example
The line plot shows the goals scored in each match: 1 goal at 3 marks, 2 goals at 2 marks, 3 goals at 3 marks and 4 goals at 1 mark. How many goals were scored altogether?
Step 1: work out the goals for each value. 1 × 3 = 3, 2 × 2 = 4 and 3 × 3 = 9 and 4 × 1 = 4.
Step 2: add the four parts. 3 + 4 = 7, 7 + 9 = 16 and 16 + 4 = 20.
Step 3: check the count of marks. 3 + 2 + 3 + 1 = 9 matches, which is one goal total per match.
Step 4: label the answer. The values are goals, so the total is 20 goals.
Answer: 20 goals.
Watch out for this
Each X is one item, not one stack. Counting the stacks instead of the marks gives a smaller number than the real total, and adding the values without multiplying by the number of marks leaves out the items that share a value.
Remember
- The number line shows the values, and one X stands for one item.
- The tallest stack is the value that happens most often.
- Add the height of every stack to count all the items.
- To find a total, multiply each value by its number of marks, then add.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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The line plot shows shoe sizes. How many children have size 5?
Show answer
3 children. There are 3 X marks above the 5.
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The shoe sizes are 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7 and 8. Which size is most common?
Show answer
Size 6. It has the tallest stack, with 5 X marks.
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The line plot has 4 at 1 mark, 5 at 3 marks, 6 at 5 marks, 7 at 2 marks and 8 at 1 mark. How many children are in the class?
Show answer
12 children. 1 + 3 + 5 + 2 + 1 = 12.
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The plot shows size 8 with 1 mark and size 4 with 1 mark. How many children have size 8?
Show answer
1 child. There is one X mark above the 8.
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Size 6 has 5 marks and size 7 has 2 marks. How many more children have size 6?
Show answer
3 children. 5 - 2 = 3.
Puzzle · Line plot riddle
Puzzle time
This line plot shows the number of pets in each home. Which number of pets happens most often?
Show a hint
The most common value is the value with the tallest stack of X marks.
Show the answer
Answer: 2. The stack above 2 has 4 X marks, which is taller than every other stack, so 2 pets is the most common number.