TX-DUSA-6 MTXESE051676 U6M17L5 Combined · Math On the Spot my.hrw.com Math Trainer Online...
Transcript of TX-DUSA-6 MTXESE051676 U6M17L5 Combined · Math On the Spot my.hrw.com Math Trainer Online...
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Red Blue Black
Shirts Ordered on One Day
White Green
EXPLORE ACTIVITY
ESSENTIAL QUESTION
Describing Categorical DataSome data are quantitative, such as height or number of siblings of all students
in a class. Other data are qualitative, such as eye color or favorite type of music.
Categorical data are data that are sorted into categories on the basis of
qualitative characteristics.
You can use the mode to summarize or describe categorical data. The mode of
a categorical data set is the category that occurs most often. If all categories have
the same frequency, there is no mode.
Karl sells red, blue, black, white, and green shirts online. One day Karl
received orders for 4 red, 5 blue, 6 black, 6 white, and 3 green shirts.
Complete the dot plot of Karl’s shirt orders for the day.
Which shirt color or colors were the most and least popular that day?
Identify the mode(s) of the data.
Reflect 1. Justify Reasoning Is it possible to find the mean or median of Karl’s
data set? Explain.
A
B
C
L E S S O N
17.5 Categorical Data
How can you summarize and describe categorical data?
Math TalkMathematical Processes
6.12.D
Measurement and data—6.12.D Summarize categorical data with numerical and graphical summaries, including the mode, … relative frequency table, and the percent bar graph, and use these … to describe the data distribution.
Could the colors in the dot plot be displayed in a
different order? Would this change the overall
results? Explain.
511Lesson 17.5
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Summarizing Categorical Data with a Relative Frequency TableIn the Explore Activity, you plotted how many times a particular color shirt was ordered. The number of times a color was ordered is called its frequency.
The relative frequency of a category is the ratio of its frequency to the sum
of the frequencies for all categories. Relative frequency is often written as a
fraction or a percent. For example, because 6 out of 24 orders were for black
shirts, the relative frequency of black shirts is or 25%.
The table shows the results of a survey of students about their favorite
summer sport. Make a relative frequency table of the data.
Favorite Summer Sport
Sport basketball baseball swimming soccer track softball
Frequency 5 7 4 3 2 4
Find the sum of the frequencies for all categories.
5 + 7 + 4 + 3 + 2 + 4 = 25
Make a frequency table. Write the relative frequency of each
category as a fraction of the total, 25, and as a percent.
Favorite Summer Sport
Sport basketball baseball swimming soccer track softball
Relative Frequency
6 __ 24
EXAMPLE 1
STEP 1
STEP 2
4 __ 25
= 16% 4 __ 25
= 16% 3 __ 25
= 12% 2 __ 25
= 8% 7 __ 25
= 28% 5 __ 25
= 20%
2. Chuy has 40 dimes, 20 pennies, 10 nickels, and 10 quarters in his coin jar.
Make a relative frequency table of the coins in the jar.
Coins in a Jar
Type of coin
Relative frequency
YOUR TURN
Math TalkMathematical Processes
6.12.D
What is the sum of the relative frequencies in
fraction form? in percent form? Why?
Multiply numerator and denominator by 4: 5 × 4 ______ 25 × 4 = 20 ____ 100 = 20%.
512 Unit 6
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35
30
25
20
15
10
5
0
Rela
tive
freq
uen
cy (
%)
Instrument
drums guitar bass saxo-phone
trumpet clarinet
Music Class Survey Results
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Using a Percent Bar Graph to Describe a Data DistributionYou can graph relative frequencies in a percent bar graph to help you visualize
how the data are distributed.
The table shows the results of a survey taken in Mr. Jenk’s music class
about the students’ favorite musical instruments. Make a percent bar
graph. Then find the mode and describe how the data are distributed.
Favorite Musical Instrument
Instrument drums guitar bass saxophone trumpet clarinet
Frequency 6 5 3 3 2 1
Relative frequency
= 30% = 25% = 15% = 15% = 10% = 5%
Make a percent bar graph of the relative frequencies. The height of each
bar shows the percent of students surveyed who favor that instrument.
The instrument mentioned most often is drums, so the mode is
drums, although the guitar is nearly as popular. More than half the
students (55%) favor drums or the guitar. About a third of students
(30%) favor the bass or saxophone. All other students (15%) favor
the trumpet or clarinet.
Reflect 3. Analyze Relationships Why is it helpful to arrange the categories in
the order of their relative frequencies?
EXAMPLEXAMPLE 2
6 __ 20
5 __ 20
3 __ 20
3 __ 20
2 __ 20
1 __ 20
STEP 1
STEP 2
6.12.D
The saxophone is the favorite musical instrument of 15% of the students surveyed.
513Lesson 17.5
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Reading Movies Sports
Favorite Summer Activities
Travel
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10
Toma
toes
Kale
Strawbe
rries
Zucchini
Melons
30
40
20
Summer Garden Plots
Plant
Rela
tive
freq
uenc
y (%
)
Devon’s Tulips50
40
30
20
10
0Rela
tive
freq
uenc
y (%
)
Tulip ColorRed Yellow Purple
4. Devon is growing tulips in his garden. He has
24 red tulips, 11 yellow tulips, and 15 purple
tulips. Make a percent bar graph and describe
the distribution.
YOUR TURN
Guided Practice
Mrs. Valentine surveyed her class about their favorite
summer activity. Four students chose reading, 7 chose
movies, 7 chose sports, and 5 chose travel. (Explore Activity)
1. Make a dot plot of the data.
2. Identify the mode(s) of the data set.
The garden club is planning their spring and summer garden. They have
20 plots. Tomatoes will be in 3 plots, kale will be in 5 plots, strawberries
will be in 6 plots, zucchini will be in 2 plots, and melons will be in 4 plots.
(Examples 1 and 2)
3. Make a relative frequency table of the data that shows both fractions
and percents.
Summer Garden Plots
Plant tomatoes kale strawberries zucchini melons
Relative frequency
4. Make a percent bar graph of the relative frequencies of the
garden plots.
5. How can you calculate relative frequencies as percents?
ESSENTIAL QUESTION CHECK-IN??
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Gerbil Fish Mouse Lizard
Name Class Date
Independent Practice17.5
Mr. Anderson’s fifth grade class is getting a class pet. Seven students vote
to get a gerbil, 3 vote for a fish, 6 vote for a mouse, and 4 vote for a lizard.
6. What is the mode of the data set? What does it mean for this situation?
7. If each pet had received 9 votes, what would the mode have been?
8. Analyze Relationships Make a dot plot of the data. Use the dot plot to
describe the data.
9. The service club sells snacks at school basketball games. In the first
quarter they sell 6 servings of nachos, 4 bags of popcorn, 7 pieces of fruit,
and 3 bags of nuts.
a. Make a relative frequency table. Include both fractions and percents.
Snacks Sold in the First Quarter
Snack nachos popcorn fruit nuts
Relative frequency
b. Analyze Relationships Deloria says she can find the relative
frequency of nuts based on another relative frequency. What might
she be doing?
c. Draw Conclusions If 9 bags of popcorn were sold rather than 4,
which relative frequencies would be affected? Explain.
6.12.D
515Lesson 17.5
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Work Area
Eye Colors
Blue5%
Brown60%
Green16%
Hazel19%
Rela
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freq
uenc
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)
Colorgreen blue brown hazel
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Eye ColorThe percent bar graph shows the relative frequencies that
resulted from of a survey about eye color.
10. Draw Conclusions Can you tell from the bar graph how many
people were surveyed? Why or why not?
11. Communicate Mathematical Ideas Describe how the data
are distributed.
12. What If? Suppose 250 people were surveyed to create the eye
color data shown in the graph for Exercises 10 and 11. How
many people would have brown eyes? Justify your answer.
13. Multiple Representations Describe how this circle graph is
similar to and different from the percent bar graph shown for
Exercises 10–11.
14. Justify Reasoning Jayshree says the number of dots in a dot plot for
Exercise 8 shows that the data is numeric and not categorical. Is she right?
Explain. If not, what is her mistake?
FOCUS ON HIGHER ORDER THINKING
Unit 6516
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