Line Graphs & Stem and Leaf Plots Lessons 6.7 and 6.9

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

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

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.

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

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

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 1650 1670 1690 1700 Year

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

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 1996 1998 2000 2002 Year

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 1999 through 2002? increase

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

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

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 1985 1990 1995 2000 $10 $20 $30 $40 Price of Stock Step 4: Title the graph and label both axes. Include a key. Year

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

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 1985 1990 1995 2000 $10 $20 $30 $40 Price of Stock Step 4: Title the graph and label both axes. Include a key. Year

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.

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 83 84 86 86 88 Step 2: Order the data from least to greatest. 91 94 99

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

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 83 84 86 86 88 91 94 99 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 3 4 6 6 8 9 1 4 9 Key: 7 5 means 75

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

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. 61 64 67 72 74 76 79 Step 2: Order the data from least to greatest. 83 84 88

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. 61 64 67 72 74 76 79 83 84 88 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 1 4 7 7 2 4 6 9 8 3 4 8 Key: 6 1 means 61

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 0 0 1 5 7 The greatest stem and greatest leaf give the greatest value, 94. 5 1 1 2 4 6 3 3 3 5 9 9 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

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 0 0 1 5 7 5 1 1 2 4 6 3 3 3 5 9 9 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

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 0 2 5 6 8 1 1 3 4 4 5 6 9 9 9 1 2 4 5 6 9 1 5 Key: 3 0 means 30

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 0 2 5 6 8 The greatest stem and greatest leaf give the greatest value, 85. 4 1 1 3 4 5 4 5 6 9 9 9 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

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 0 2 5 6 8 4 1 1 3 4 5 4 5 6 9 9 9 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

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

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

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.

6. Make a stem-and-leaf plot of the data. Lesson Quiz: 6. Make a stem-and-leaf plot of the data. 42 36 40 31 29 49 21 28 52 27 22 35 30 46 34 34 2 1 2 7 8 9 3 0 1 4 4 5 6 4 0 2 6 9 5 2 Stems Leaves Key: 3 | 0 means 30

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