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

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

Course 2


Course 2


Course 2

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


Course 2

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.


Course 2

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.


Course 2

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.


Course 2

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

Additional Example 1: Organizing and Interpreting Data in a Frequency Table

February Temperatures in 20 CitiesAverage

HighsFrequency

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


Course 2


69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2

Additional Example 1 Continued

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column.


HighsFrequency


7

5

5

3

0–19

20–39

40–59

60–79


Course 2


69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2


Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.


HighsFrequency


0–19

20–39

40–59

60–79

7

5

5

3

7

12

17

20

17 cities had average high temperature below 59 degrees.


Course 2

Check It Out: Example 1

English Exam GradesGrades Frequenc

yCumulative Frequency

60–69

70–79

80–89

90–99

Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals.

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


Course 2


85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96

Check It Out: Example 1 Continued

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column.



60–69

70–79

80–89

90–99

4

4

6

6


Course 2


85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96

Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.



60–69

70–79

80–89

90–99

4

4

6

6

48

14

20

8 students received grades of 79 or below.



Course 2

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

Additional Example 2: Organizing and Interpreting Data in a Stem-and-Leaf Plot

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.


Course 2


Step 2: List the stems from least to greatest on the plot.

Stems Leaves

1

2

3

4

The stems are the tens digits.


33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17


Course 2


Step 3: List the leaves for each stem from least to greatest.

Stems Leaves

1

2

3

4


2 5 5 7 7 8

0 1 2 3 3 93 3

0

The leaves are the ones digits.


33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17


Course 2


Step 4: Add a key and a title.


Stems Leaves

1

2

3

4

2 5 5 7 7 8

0 1 2 3 3 93 3

0


Number of Years Coached

Key: 2 | 1 means 21.

11 coaches coached fewer than 25 years.


Course 2

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

Check It Out: Example 2

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.


Course 2


Step 2: List the stems from least to greatest on the plot.

Stems Leaves

2

3

4

5

6



55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41


Course 2



Stems Leaves

2

3

4

5

6

Step 3: List the leaves for each stem from least to greatest.


3 7 8 90 0 3 5 7

0 1 1 3 55

0 1 2 8

8


55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41


Course 2



Step 4: Add a key and a title.


Stems Leaves

2

3

4

5

6

3 7 8 90 0 3 5 7

0 1 1 3 55

0 1 2 8

8

Number of times a Soccer Player can bounce the ball on their knee


12 soccer players can bounce the ball on their knee more than 36 times.


Course 2

Make a line plot of the data. How many hours per day did Morgan babysit most often?

Additional Example 3: Organizing and Interpreting Data in a Line Plot

M T W Th F S Su

Wk 1 0 6 4 6 5 8 2

Wk 2 2 7 7 7 0 6 8

Wk 3 0 6 8 5 6 1 2

Wk 4 4 8 4 3 3 6 0

Number of Babysitting Hours in July


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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


Course 2



Step 2: Put an X above the number on the number line that corresponds to the number of babysitting hours in July.

0 1 2 3 4 5 6 7 8

XXXX

X

XXX XX

XXX XX

XXXXXX

XXX

XXXX

The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.


Course 2

Make a line plot of the data. How many slices of pizza did most people eat?

Check It Out: Additional Example 3

2 4 1 2 5 3 1

0 4 3 2 5 3 2

4 6 1 4 2 2 5

Number of Slices eaten per Person


Course 2


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

Make a line plot of the data. How many slices of pizza did most people eat?


Course 2


0 1 2 3 4 5 6

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.

X

XXX

XXXXXX

XXX

XXXX XX

XX

The greatest number of X’s appear above the number 2. This means that most people ate 2 slices of pizza.


Course 2

Lesson Quiz: Part I

Nurses’ Ages

Ages Frequency


20–29 5 5

30–39 7 12

40–49 4 16

50–59 2 18

60–69 2 20

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


Course 2


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?

Stems Leaves

2

3

4

5

6

1 3 3 4 41 3 4 5 5 8 9

2 5 5 5 7 7 0 1

Nurses’ Ages


4

Lesson Quiz: Part II


Course 2


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

20-29 30-39 40-49 50-59 60-69

XXXXX

XXXXXXX

XXXX

XX

XX

Lesson Quiz: Part III

Documents

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