Frequency Tables, Stem-and-Leaf Plots, and Line Plots 7-1 Course 2

Learn to organize and interpret data in frequency tables and stem-and-leaf plots, and line plots.

Cumulative frequency is the total of a frequency and all the frequencies below it in a frequency table. It is a running total of the frequencies in each category. You determine the cumulative frequency by adding the top frequency to the next frequency, and then to the next frequency, and so on. The total number in your cumulative frequency should equal the total number of data in your table.

A stem-and-leaf plot is a plot where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits). For example "32" would be split into "3" (stem) and "2" (leaf). The stem is the number in the tens place. Stems can occur several times, but they are only listed once. The leaves are the numbers in the ones place. Leaves can occur several times, and should be listed each time they occur.

Usually uses Xs above the numbers. A line plot is a graph that shows frequency (how often something happens) of data along a number line. Usually uses Xs above the numbers. Each X stands for 1. It is almost like a very simple bar graph.

Additional Example 1: Organizing and Interpreting Data in a Frequency Table The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals. 0–19 20–39 40–59 60–79

Additional Example 1 Continued The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. 0–19 7 20–39 5 40–59 5 60–79 3

Additional Example 1 Continued The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency 0–19 20–39 40–59 60–79 7 5 3 Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 7 12 17 20 17 cities had average high temperature below 59 degrees.

Check It Out: Example 1 60–69 70–79 80–89 90–99 The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below? 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 English Exam Grades Grades Frequency Cumulative Frequency Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals. 60–69 70–79 80–89 90–99

Check It Out: Example 1 Continued The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below? 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 English Exam Grades Grades Frequency Cumulative Frequency 60–69 70–79 80–89 90–99 Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. 4 4 6 6

Check It Out: Example 1 Continued The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below? 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 English Exam Grades Grades Frequency Cumulative Frequency 60–69 70–79 80–89 90–99 4 6 Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 4 8 14 20 8 students received grades of 79 or below.

Additional Example 2: Organizing and Interpreting Data in a Stem-and-Leaf Plot The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 1: Order the data from least to greatest. Since the data values range from 12 to 40, use tens digits for the stems and ones digits for the leaves.

Additional Example 2 Continued The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 2: List the stems from least to greatest on the plot. Stems Leaves The stems are the tens digits. 1 2 3 4

Additional Example 2 Continued The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 3: List the leaves for each stem from least to greatest. Stems Leaves The stems are the tens digits. The leaves are the ones digits. 2 5 5 7 7 8 1 2 3 4 1 2 3 3 9 3 3

Additional Example 2 Continued Step 4: Add a key and a title. Stems Leaves 1 2 3 4 5 7 8 9 Number of Years Coached The stems are the tens digits. The leaves are the ones digits. Key: 2 | 1 means 21. 11 coaches coached fewer than 25 years.

Check It Out: Example 2 Step 1: The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times. 55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41 Step 1: Order the data from least to greatest. Since the data values range from 23 to 68, use tens digits for the stems and ones digits for the leaves.

Check It Out: Example 2 Continued The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times. 55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41 Step 2: List the stems from least to greatest on the plot. Stems Leaves The stems are the tens digits. 2 3 4 5 6

Check It Out: Example 2 Continued The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times. 55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41 Step 3: List the leaves for each stem from least to greatest. Stems Leaves 2 3 4 5 6 The stems are the tens digits. The leaves are the ones digits. 3 7 8 9 3 5 7 8 1 1 3 5 5 1 2 8

Number of times a Soccer Player can bounce the ball on their knee Check It Out: Example 2 Continued Step 4: Add a key and a title. Number of times a Soccer Player can bounce the ball on their knee Stems Leaves 2 3 4 5 6 7 8 9 1 The stems are the tens digits. The leaves are the ones digits. Key: 4 | 0 means 40. 12 soccer players can bounce the ball on their knee more than 36 times.

Additional Example 3: Organizing and Interpreting Data in a Line Plot Make a line plot of the data. How many hours per day did Morgan babysit most often? Number of Babysitting Hours in July M T W Th F S Su Wk 1 6 4 5 8 2 Wk 2 7 Wk 3 1 Wk 4 3

Additional Example 3 Continued Make a line plot of the data. How many hours per day did Morgan babysit most often? Step 1: The data values range from 0 to 8. Draw a number line that includes this range. 0 1 2 3 4 5 6 7 8

Additional Example 3 Continued Make a line plot of the data. How many hours per day did Morgan babysit most often? Step 2: Put an X above the number on the number line that corresponds to the number of babysitting hours in July. XXXXXX XXXX XXXX XXX XXX XXX XX XX X 0 1 2 3 4 5 6 7 8 The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.

Check It Out: Additional Example 3 Make a line plot of the data. How many slices of pizza did most people eat? Number of Slices eaten per Person 2 4 1 5 3 6

Check It Out: Example 3 Continued Make a line plot of the data. How many slices of pizza did most people eat? Step 1: The data values range from 0 to 6. Draw a number line that includes this range. 0 1 2 3 4 5 6

Check It Out: Example 3 Continued Make a line plot of the data. How many slices of pizza did most people eat? Step 2: Put an X above the number on the number line that corresponds to the number slices of pizza eaten per person. XXXXXX XXXX XXX XXX XXX X X 0 1 2 3 4 5 6 The greatest number of X’s appear above the number 2. This means that most people ate 2 slices of pizza.

Lesson Quiz: Part I The data shows the ages of some hospital nurses. 33, 35, 23, 39, 23, 24, 34, 21, 57, 45, 57, 60, 45, 24, 31, 42, 61, 45, 35, 38 1. Make a cumulative frequency table of the data. How many of the nurses are under the age of 40? 12 Nurses’ Ages Ages Frequency Cumulative Frequency 20–29 5 5 30–39 7 12 40–49 4 16 50–59 2 18 60–69 2 20

Lesson Quiz: Part II Nurses’ Ages Stems Leaves 1 3 3 4 4 2 3 4 The data shows the ages of some hospital nurses. 33, 35, 23, 39, 23, 24, 34, 21, 57, 45, 57, 60, 45, 24, 31, 42, 61, 45, 35, 38 2. Make a stem-and-leaf plot of the data. How many nurses are over the age of 45? 4 Stems Leaves 2 3 4 5 6 1 3 3 4 4 1 3 4 5 5 8 9 2 5 5 5 7 7 0 1 Nurses’ Ages Key: 4 | 2 means 42.

Lesson Quiz: Part III The data shows the ages of some hospital nurses. 33, 35, 23, 39, 23, 24, 34, 21, 57, 45, 57, 60, 45, 24, 31, 42, 61, 45, 35, 38 3. Make a line plot of the data. What age occurs most often? 45 XXXXXXX XXXXX XXXX XX XX 20-29 30-39 40-49 50-59 60-69