Frequency Tables and StemandLeaf Plots

1
Frequency Tables and Stem-and-Leaf Plots
1-3
Warm Up
Problem of the Day
Lesson Presentation
Course 2
2
Warm Up Use these numbers to answer the following
questions. 136, 151, 104, 168, 140,
124, 162, 121, 118 1. What is the highest
score? 2. What is the lowest score? 3. What is
the range of scores? 4. How can you find the
median?
168
104
64
Arrange the numbers in order and find the value
in the middle.
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Frequency Tables and Stem-and-Leaf Plots
Problem of the Day Books A, B, C, and D are on
the bookshelf. A is between C and B. B is between
A and D. D is not on the right. What is the order
of the books from right to left?
D, B, A, C
Course 2
4
Learn to organize and interpret data in frequency
tables and stem-and-leaf plots.
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Vocabulary
frequency table cumulative frequency stem-and-leaf
plot
6
A frequency table is a way to organize data into
categories or groups.
By including a cumulative frequency column in
your table, you can keep a running total of the
frequencies in each category.
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Additional Example 1
Organizing 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. 69, 66, 65, 51, 50,
50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4,
2, 2
Step 1 Look at the range to choose equal
intervals for the data.
019
2039
4059
6079
8
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. 69, 66, 65, 51, 50,
50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4,
2, 2
Step 2 Find the number of data values in each
interval. Write these numbers in the Frequency
column.
7
5
5
3
9
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. 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.
7
12
17
20
10
Try This Example 1
The list shows the grades received on an English
exam. Make a cumulative frequency table of the
data. 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60,
66, 94, 86, 79, 87, 68, 95, 71, 96
Step 1 Look at the range to choose equal
intervals for the data.
6069
7079
8089
9099
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Try This Example 1 Continued
The list shows the grades received on an English
exam. Make a cumulative frequency table of the
data. 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60,
66, 94, 86, 79, 87, 68, 95, 71, 96
Step 2 Find the number of data values in each
interval. Write these numbers in the Frequency
column.
4
4
6
6
12
Try This Example 1 Continued
The list shows the grades received on an English
exam. Make a cumulative frequency table of the
data. 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.
4
8
14
20
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A stem-and-leaf plot can be used to show how
often data values occur and how they are
distributed. Each leaf on the plot represents the
right-hand digit in a data value, and each stem
represents left-hand digits.
Key 27 means 27
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Additional Example 2
Organizing 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. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17,
15, 15, 12, 17
Step 1 Find the least data value
and the greatest data value.
Since the data values range from 12 to 40, use
tens digits for the stems and ones digits for the
leaves.
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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. 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.
The stems are the tens digits.
1 2 3 4
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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. 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.
The stems are the tens digits.
The leaves are the ones digits.
5
5
7
7
8
2
1 2 3 4
0
3
1
2
3
9
3
3
0
17
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. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17,
15, 15, 12, 17
Step 4 Add a key and a title.
Number of Years Coached
The stems are the tens digits.
The leaves are the ones digits.
Key 2 1 means 21.
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Try This Example 2
The list shows the number of students on twenty
school buses. 55, 60, 33, 30, 23, 45, 28, 41, 62,
29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41
Step 1 Find the least data value
and the greatest data value.
Since the data values range from 23 to 68, use
tens digits for the stems and ones digits for the
leaves.
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Try This Example 2 Continued
The list shows the number of students on twenty
school buses. 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.

The stems are the tens digits.
2 3 4 5 6
20
Try This Example 2 Continued
The list shows the number of students on twenty
school buses. 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.

The stems are the tens digits.
The leaves are the ones digits.
8
3
7
9
0
0
3
7
8
5
0
1
1
3
5
5
1
2
8
0
21
Try This Example 2 Continued
The list shows the number of students on twenty
school buses. 55, 60, 33, 30, 23, 45, 28, 41, 62,
29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41
Step 4 Add a key and a title.

Number of Students on School Buses
The stems are the tens digits.
The leaves are the ones digits.
Key 4 0 means 40.
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Lesson Quiz
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. 2. Make
a stem-and-leaf plot of the data.
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Lesson Quiz
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.
24
Lesson Quiz
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.
Key 4 2 means 42.