Transcript 6-5

6-5 Frequency Tables and Histograms
Warm Up
Problem of the Day
Lesson Presentation
Course 1
6-5 Frequency Tables and Histograms
Warm Up
Create a bar graph of the data.
Favorite rides at fair:
Ferris wheel = 5,
loop the loop = 4,
merry-go-round = 3,
bumper cars = 7,
sit and spin = 9
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Favorite Rides at Fair
10
8
6
4
2
0
Ferris Wheel Loop the loop
Merry-goround
Bumper cars
Sit and spin
6-5 Frequency Tables and Histograms
Problem of the Day
A set of 7 numbers has a mean of 36, a
median of 37, a mode of 37, and a range
of 6. What could the 7 numbers be?
Possible answer: 33, 33, 36, 37, 37, 37, 39
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6-5 Frequency Tables and Histograms
Learn to organize data in frequency tables
and histograms.
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6-5 Frequency
Insert Lesson
Title
Here
Tables
and
Histograms
Vocabulary
frequency table
cumulative frequency
histogram
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6-5 Frequency Tables and Histograms
Additional Example 1: Making a Tally Table
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
most students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
whorl
loop
Make a tally table to organize the data.
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6-5 Frequency Tables and Histograms
Additional Example 1 Continued
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
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whorl
loop
Step 1: Make a column for
each fingerprint pattern.
6-5 Frequency Tables and Histograms
Additional Example 1 Continued
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
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whorl
loop
Step 1: Make a column for
each fingerprint pattern.
Step 2: For each fingerprint,
make a tally mark in the
appropriate column.
6-5 Frequency Tables and Histograms
Reading Math
A group of four tally marks with a line
through it means five.
llll = 5
llll llll = 10
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6-5 Frequency Tables and Histograms
Additional Example 1 Continued
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
whorl
loop
Step 1: Make a column for
each fingerprint pattern.
Step 2: For each fingerprint,
make a tally mark in the
appropriate column.
Number of Fingerprint Patterns
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6-5 Frequency Tables and Histograms
Try This: Example 1
Students in Ms. Gracie’s class recorded their
pets. Which type of pets do more students in
Ms. Gracie’s class have?
dog
cat
dog
cat
fish
dog
cat
dog
cat
dog
dog
fish
fish
dog
fish
cat
Make a tally table to organize the data.
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6-5 Frequency Tables and Histograms
Try This: Example 1 Continued
Students in Ms. Gracie’s class recorded their
pets. Which type of pet do more students in Ms.
Gracie’s class have?
dog
cat
dog
cat
fish
dog
cat
dog
cat
dog
dog
fish
fish
dog
fish
cat
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Step 1: Make a column for
each pet pattern.
6-5 Frequency Tables and Histograms
Try This: Example 1 Continued
Students in Ms. Gracie’s class recorded their
pet. Which type of pet do more students in Ms.
Gracie’s class have?
dog
cat
dog
cat
fish
dog
cat
dog
cat
dog
dog
fish
fish
dog
fish
cat
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Step 1: Make a column for
each pet.
Step 2: For each pet, make a
tally mark in the appropriate
column.
6-5 Frequency Tables and Histograms
Try This: Example 1 Continued
Students in Ms. Gracie’s class recorded their
pets. Which type of pet do more students in Ms.
Gracie’s class have?
dog
cat
dog
cat
fish
dog
cat
dog
cat
dog
dog
fish
fish
dog
fish
cat
Step 1: Make a column for
each pet.
Step 2: For each pet, make a
tally mark in the appropriate
column.
Number of Pets
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6-5 Frequency Tables and Histograms
Try This: Example 1 Continued
Students in Ms. Gracie’s class recorded their
pets. Which type of pet do more students in Ms.
Gracie’s class have?
dog
cat
dog
cat
fish
dog
cat
dog
cat
dog
dog
fish
fish
dog
fish
cat
Most students in Ms.
Gracie’s class have a
dog.
Number of Pets
Dog
7
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Fish
4
Cat
5
6-5 Frequency Tables and Histograms
A frequency table tells the
number of times an event,
category, or group occurs.
The cumulative frequency
column shows a running total of
all frequencies.
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6-5 Frequency Tables and Histograms
Additional Example 1 Continued
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
whorl
Most students in Mr.
Ray’s class have an
arch fingerprint.
loop
Number of Fingerprint Patterns
Whorl
llll
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Arch
llll l
Loop
llll
6-5 Frequency Tables and Histograms
Additional Example 2: Making a Cumulative
Frequency Table
Use the tally table in Additional Example 1 to make a
cumulative frequency table.
Step 1: Make a row for each pattern.
Step 2: The frequency is how many
times each pattern occurred.
Step 3: Find the cumulative frequency for each row
by adding all frequency values above or in that row.
Number of Fingerprint Patterns
Fingerprint Pattern
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Whorl
Frequency
5
Cumulative Frequency
5
Arch
6
11
Loop
5
16
6-5 Frequency Tables and Histograms
Try This: Additional Example 2
Use the tally table in Try This: Example 1 to make a
cumulative frequency table.
Step 1: Make a row for each pattern.
Step 2: The frequency is how many
times each pattern occurred.
Step 3: Find the cumulative frequency for each row
by adding all frequency values above or in that row.
Number of Pets
Pet
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Dog
Frequency
7
Cumulative Frequency
7
Fish
4
11
Dog
5
16
6-5 Frequency Tables and Histograms
Additional Example 3: Making a Frequency Table
with Intervals
Use the data in the table to make a frequency
table with intervals.
Number of Pages Read per Student Last Weekend
12
5
15
22
40
34
19
37
7
18
Step 1: Choose equal intervals.
Step 2: Find the number of data values in each
interval. Write these numbers in the
“Frequency” row.
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6-5 Frequency Tables and Histograms
Additional Example 3 Continued
Number of Pages Read per Student Last Weekend
12
5
15
22
40
34
19
37
7
18
Number of Pages Read per Student Last Weekend
Number
Frequency
This table shows that 2 students read between 1
and 10 pages, 4 students read between 11 and
20 pages, and so on.
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6-5 Frequency Tables and Histograms
Try This: Example 3
Use the data in the table to make a frequency
table with intervals.
Number of Miles Walked Last Week
17
29
9
19
7
5
27
34
21
38
Step 1: Choose equal intervals.
Step 2: Find the number of data values in each
interval. Write these numbers in the
“Frequency” row.
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6-5 Frequency Tables and Histograms
Try This: Example 3 Continued
Number of Miles Walked Last Week
17
29
9
19
7
5
27
34
21
38
Number of Miles Walked Last Week
Number
Frequency
This table shows that 3 students walked between
1 and 10 miles, 2 students walked between 11
and 20 miles, and so on.
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6-5 Frequency Tables and Histograms
A histogram is a graph that
shows the number of data items
that occur within each interval. It
is similar to a bar graph, but the
bars touch.
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6-5 Frequency Tables and Histograms
Additional Example 4: Making a Histogram
Use the frequency table in Additional Example 3 to make a
histogram.
Step 1: Choose an appropriate scale and interval.
Step 2: Draw a bar for the number of students in
each interval. The bars should touch but not overlap.
Step 3: Title the graph
and label the axes.
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6-5 Frequency Tables and Histograms
Try This: Example 4
Use the frequency table in Try This: Example 3 to make a
histogram.
Step 1: Choose an appropriate scale and interval.
Step 2: Draw a bar for the number of students in
each interval. The bars should touch but not overlap.
Step 3: Title the graph
and label the axes.
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6-5 Frequency
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Histograms
Lesson Quiz: Part 1
1. Students listed the number of days they spent
on vacation in one year. Make a tally table with
intervals of 5.
2, 18, 5, 15, 7, 10, 1, 10, 4
16, 7, 11, 17, 3, 8, 14, 13, 10
Number of Days Spent on Vacation
1–5
6–10
11–15
16–20
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6-5 Frequency
Insert Lesson
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and
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Histograms
Lesson Quiz
2. Use your tally table from problem 1 to make a
frequency and cumulative frequency table.
Number of Days Spent on Vacation
Cumulative
Number of Days Frequency Frequency
1–5
5
5
6–10
6
11
11–15
4
15
16–20
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3
18