1. Line Graphs & Stem and Leaf Plots
Lessons 6.7 and 6.9

2. Learn to display and analyze data in line graphs.
Learn to make and analyze stem-and- leaf plots.

3. Vocabulary
line graph
double-line graph
stem-and-leaf plot

4. Data that shows change over time is best displayed in a line graph
Data that shows change over time is best displayed in a line graph. A line graph displays a set of data using line segments.

5. Population of New Hampshire
Example 1: Making a Line Graph
Use the data in the table to make a line graph.
5,000
1700
4,200
1690
1,800
1670
1,300
1650
Population
Year
Population of New Hampshire

6. Because time passes whether or not the population changes, time is independent of population. Always put the independent quantity on the horizontal axis.
Caution!

7. Population of New Hampshire
Example 1 Continued
Step 1: Place year on the horizontal axis and population on the vertical axis. Label the axes.
Step 2: Determine an appropriate scale and interval for each axis.
Population of New Hampshire
Step 3: Mark a point for each data value. Connect the points with straight lines.
6,000
5,000
4,000
Population
3,000
2,000
Step 4: Title the graph.
1,000
Year

8. School District Enrollment
White board practice:
Use the data in the table to make a line graph.
6,000
2002
5,200
2000
2,800
1998
2,300
1996
Population
Year
School District Enrollment

9. School District Enrolment
White board practice: Solution
Step 1: Place year on the horizontal axis and number of students on the vertical axis. Label the axes.
Step 2: Determine an appropriate scale and interval for each axis.
School District Enrolment
6,000
Step 3: Mark a point for each data value. Connect the points with straight lines.
5,000
4,000
Number of Students
3,000
2,000
Step 4: Title the graph.
1,000
Year

10. Example 2: Reading a Line Graph
Use the line graph to answer each question.
In which year did CDs cost the most?
2002
About how much did CDs cost in 2000?
$15
Did CD prices increase or decrease from through 2002?
increase

11. Line graphs that display two sets of data are called double-line graphs.

12. Example 3: Making a Double-Line Graph
Use the data in the table to make a double- line graph.
$21
$31
$35
$38
Corporation B
$33
$34
$20
$16
Corporation A
2000
1995
1990
1985
Stock Prices
Use different colors of lines to connect the stock values so you will easily be able to tell the data apart.
Helpful Hint

13. Example 3 Continued
Step 1: Determine an appropriate scale and interval.
Step 2: Mark a point for each Corporation A value and connect the points.
Corp. A
Corp. B
Step 3: Mark a point for each Corporation B value and connect the points.
Stock Prices $0
$10
$20
$30
$40
Price of Stock
Step 4: Title the graph and label both axes. Include a key.
Year

14. Stock Prices White board practice:
Use the data in the table to make a double-line graph. $7
$14
$22
$35
Corporation D
$28
$20
$16 $8
Corporation C
2000
1995
1990
1985
Stock Prices

15. White board practice: Solution
Step 1: Determine an appropriate scale and interval.
Step 2: Mark a point for each Corporation C value and connect the points.
Corp. C
Corp. D
Step 3: Mark a point for each Corporation D value and connect the points.
Stock Prices $0
$10
$20
$30
$40
Price of Stock
Step 4: Title the graph and label both axes. Include a key.
Year

16. A stem-and-leaf plot shows data arranged by place value
A stem-and-leaf plot shows data arranged by place value. You can use a stem-and-leaf plot when you want to display data in an organized way that allows you to see each value.

17. Example 4: Creating Stem-and-Leaf Plots
Use the data in the table to make a stem-and- leaf plot. 86 79 99 84 88 94 91 83 75
Test Scores
Step 1: Group the data by tens digits.
75 79
Step 2: Order the data from least to greatest.

18. Helpful Hint
To write 42 in a stem-and-leaf plot, write each digit in a separate column.
4 2
Stem
Leaf

19. Example 4 Continued
Step 3: List the tens digits of the data in order from least to greatest. Write these in the “stems” column.
75 79
Step 4: For each tens digit, record the ones digits of each data value in order from least to greatest. Write these in the “leaves” column.
Test Scores
Stems
Leaves
Step 5: Title the graph and add a key. 7
5 9 8 9
Key: 7 5 means 75

20. White board practice:
Use the data in the table to make a stem-and- leaf plot. 67 74 76 83 84 61 79 64 88 72
Test Scores

21. White board practice: Solution
Use the data in the table to make a stem-and- leaf plot. 67 74 76 83 84 61 79 64 88 72
Test Scores
Step 1: Group the data by tens digits.
Step 2: Order the data from least to greatest.

22. White board practice: Solution
Step 3: List the tens digits of the data in order from least to greatest. Write these in the “stems” column.
Step 4: For each tens digit, record the ones digits of each data value in order from least to greatest. Write these in the “leaves” column.
Test Scores
Stems
Leaves
Step 5: Title the graph and add a key. 6 7 8
Key: 6 1 means 61

23. Example 5: Reading Stem-and-Leaf Plots
Find the least value, greatest value, mean, median, mode, and range of the data.
The least stem and least leaf give the least value, 40.
Stems
Leaves 4
The greatest stem and greatest leaf give the greatest value, 94. 5 6 7
0 4 4 8
3 6 7
Use the data values to find the mean (40 + … + 94) ÷ 23 = 64. 9
1 4
Key: 4 0 means 40

24. The median is the middle value in the table, 63.
Example 5 Continued
The median is the middle value in the table, 63.
To find the mode, look for the number that occurs most often in a row of leaves. Then identify its stem. The mode is 63.
Stems
Leaves 4 5 6 7
0 4 4
The range is the difference between the greatest and the least value. 94 – 40 = 54. 8
3 6 7 9
1 4
Key: 4 0 means 40

25. White board practice:
Find the least value, greatest value, mean, median, mode, and range of the data.
Stems
Leaves 3 4 5 6 7 8
1 2 4
5 6 9
1 5
Key: 3 0 means 30

26. White board practice: Solution
Find the least value, greatest value, mean, median, mode, and range of the data.
The least stem and least leaf give the least value, 30.
Stems
Leaves 3
The greatest stem and greatest leaf give the greatest value, 85. 4 5 6
1 2 4
Use the data values to find the mean (30 + … + 85) ÷ 23 = 55. 7
5 6 9 8
1 5
Key: 3 0 means 30

27. White board practice: Solution
The median is the middle value in the table, 56.
To find the mode, look for the number that occurs most often in a row of leaves. Then identify its stem. The mode is 59.
Stems
Leaves 3 4 5 6
1 2 4
The range is the difference between the greatest and the least value. 85 – 30 = 55. 7
5 6 9 8
1 5
Key: 3 0 means 30

28. Lesson Quiz:
Use the line graph to answer each question.
1. Which plant was taller on Tuesday?
2. Which plant grew more between Thursday and Friday?
3. Which plant grew the most in one week? A
Each grew the same amount. A

29. Lesson Quiz:
4. Use the line graph to tell the day on which Toy B was sold more than Toy A.
A. Tuesday
B. Wednesday
C. Thursday
D. Friday

30. Lesson Quiz:
5. Which of the following
statements can be inferred
from the graph?
A. Student B is taller than Student A at the age of 8 years.
B. Student A has grown taller than Student B over a period of 5 years.
C. Student B has grown taller than Student A over a period of 5 years.

31. 6. Make a stem-and-leaf plot of the data.
Lesson Quiz:
6. Make a stem-and-leaf plot of the data.
5 2
Stems
Leaves
Key: 3 | 0 means 30

32. Lesson Quiz:
Find each value using the stem-and-leaf plot.
7. What is the least value?
8. What is the mean?
9. What is the median?
10. What is the mode? 21
34.75 34 34