S
s
’
e
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s
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s
a
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WRI Cl
(6-8)
FrequencyTwo-Way
Tables
Name _________________________________ (6-8)
7.1bTwo-Way
(refine)—More
Frequency Tables
1. Mr. Smith splits pupils that did not do their homework into two categories:
first timers and second(+) timers.
a. Design a table to show how many boys and how many girls did not do their homework.
b. In one month, 36 girls and 12 boys did not do their homework for the first time. Twelve girls and 30
boys did not do their homework for the second time. Put these figures in your table.
2. Complete the two-way table for Hollywood Junior High’s eating habits.
Male
Female
Totals
Eat Breakfast regularly
190
110
300
Do not Eat Breakfast
regularly
130
165
295
320
275
595
Totals
a. Of the total males, what percentage do not eat breakfast regularly?
b. Of the total people who eat breakfast regularly, what percentage of them are males?
3. Complete the two-way table for Jersey High’s transportation survey.
Male
Female
Totals
Walk
34
46
80
Car
28
17
45
Bus
15
12
27
Cycle
52
17
69
129
92
221
Totals
a. Of the total males, what percentage cycle?
b. Of the total people who use the bus, what percentage are female?
7.1a (build)—Creating Two-Way Frequency Tables
4.
1. A bank teller splits transactions into two categories: deposits and withdrawals.
a. Design a table that he could use to show how many transactions are deposits and how many are
withdrawals.
b. In one shift, he has 72 transactions. Of those, 12 males make deposits and 30 make withdrawals. While
20 females make deposits. Put these figures in your table and complete the missing portion of the table.
2. Heather has a dance studio that offers classes in both contemporary and hip-hop dance.
5.
a. Design a table that will show the number of female and male dancers who take classical or hip-hop
classes.
b. She has 38 female hip-hop dancers and 43 male hip-hop dancers. Heather has a total of 200 dancers
enrolled in classes with 60 of them being male. Put these figures in your table and complete the missing
portion of the table.
c. How many contemporary male dancers are enrolled in her studio?
Sec Math 1 In-Sync by Jordan School District, Utah is licensed under a
3. Sarah is worried
about Commons
how much
garbage she creates each week. She
to look
at how many items
6.
Creative
Attribution-NonCommercial-ShareAlike
3.0decides
United States
License
she could recycle instead in three weeks’ time.
283
a. Design a table to show the number of cans, glass bottles, and newspapers she recycled over the last three
weeks.
b. Sarah recycled 5 cans in the 1st week, 3 in the second and 4 in the last week. She recycled 6 glass bottles
every week and 1 newspaper in the last week. In the 1st two weeks she recycled 2 and then 3
newspapers. Put these numbers in your table and complete any missing portions.
(6-8) Two-Way Frequency Tables
(6-8)
7.1c (apply)—Analyze Frequency Tables (Joint, Marginal, and Conditional)
1.
7. Copy and complete the two-way table for Hollywood Junior High’s eating habits.
Eat Breakfast regularly
Do not Eat Breakfast
regularly
Totals
Male
190
Female
110
Totals
300
130
320
165
275
295
595
a)
b)
c)
d)
e)
f)
g)
How many females “eat breakfast regularly”? (a joint frequency)
How many females were included in the survey? (a marginal frequency)
How many females eat breakfast out of the total number of females? (a conditional relative frequency)
How many people were included in this survey? (this is a marginal frequency)
How many males “do not eat breakfast regularly”? (this is a joint frequency)
How many males and females do not eat breakfast regularly? (this is a marginal frequency)
How many males do not eat breakfast out of the total number of people who do not eat breakfast?
(a conditional relative frequency)
h) Do more females eat breakfast or do more males eat breakfast? (a comparison of joint frequencies)
i) Which group of people eat breakfast more regularly?
j) Which group of people does not eat breakfast regularly?
2.
8. Below is a table showing men’s and women’s preferences of activities.
a) Looking at just the total columns (marginal frequencies),
what can we conclude about the activities?
a. Dance is more interesting.
b. They have roughly equal appeal.
Men
c. Sports is the least chosen activity.
Women
d. TV is the preferred activity.
b) Looking at the joint frequencies, we see that women
TOTAL
show a strong preference for which activity?
c) Looking at the joint frequencies, we see that men show
a strong preference for which activity?
Dance
Sports
TV
TOTAL
2
10
8
20
16
6
8
30
18
16
16
50
3.
9. Below is a table for Jersey High’s transportation survey results.
Walk
Car
Bus
Cycle
Totals
a)
b)
c)
d)
Male
34
28
15
52
129
Female
46
17
12
17
92
Totals
80
45
27
69
221
Identify one joint frequency from this table and describe its meaning.
Identify one marginal frequency from this table and describe its meaning.
Identify one conditional relative frequency from this table and describe its meaning.
Write two conclusions that you can make from this frequency table.
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284
(6-8) Two-Way Frequency Tables
(6-8)
7.1d (apply)—Relative, Joint, and Marginal Frequencies
1. The frequency table below shows the results of a survey that Carla took. She asked 40 randomly selected
10.
people what their favorite food was to eat at a baseball game. The three choices were hotdogs, hamburgers,
or pizza. Convert this table into a relative frequency table that uses decimals as well as percentages.
Preferred Food at the ball game
Frequency
Hotdogs Hamburgers Pizza Total
18
12
10
40
a. Divide the numbers in the frequency table by the total to obtain relative frequencies as decimals. Record
the results in the table below.
Preferred Food at the ball game
Hotdogs
Hamburgers Pizza Total
Sec
Math
1
In-Sync
by
Jordan
School
District,
Relative Frequency
18/40=0.45 Utah is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License
282
b. Write the decimals as percentages in the table below.
Preferred Food at the ball game Hotdogs
Relative Frequency
45%
Hamburgers Pizza
Total
c. How can you check to see if you have accurately converted frequencies to relative frequencies?
d. Explain why the number in the total column of a relative frequency table is always 1 or 100%?
e. What does the data tell us about the most preferred food to eat at a baseball game?
2. For her survey, Carla also recorded the age of each person. The results are shown in the two-way frequency
11.
table below. Each entry is the frequency of people who prefer a certain food and are in a certain age group.
Child
Teenager
Adult
Total
Hotdogs
8
5
5
Hamburgers
1
3
8
Pizza
2
5
3
Total
a. Fill in the missing marginal frequencies (the entries in the total row and total column).
b. Highlight the joint frequencies (entries in the body of the table).
c. Find the grand total, which is the sum of the row totals as well as the sum of the column totals. Write the grand
total in the lower-right corner of the table (the intersection of the total column and the total row).
d. Where have you seen the numbers in the total row before?
e. In terms of Carla's survey, what does the grand total represent?
f.
What does the data tell us about the preference of food for children at a baseball game?
g. How does this compare to adults?
h. Amongst all age groups what food would you say is most preferred?
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285
(6-8) Two-Way Frequency Tables
(6-8)
3. Make a relative frequency table for the rows and columns
12.
Relative Frequency of Rows
Child
Teenager
Adult
Total
a.
b.
c.
d.
Hotdogs Hamburgers
Relative Frequency of Columns
Pizza
Total
Child
Teenager
Adult
Total
Hotdogs Hamburgers
Pizza
Total
What is the probability that a child will choose pizza?
What is the probability that an adult will choose a hamburger?
What percentage of adults prefer hotdogs?
What percentage of teenagers prefer pizza?
4. Make a relative frequency table by calculating the relative frequency of the marginal and joint frequencies
13.
compared to the grand total. Write your relative frequencies as decimals and percentages.
Child
Teenager
Adult
Total
Hotdogs
Hamburger
Pizza Total
a. Highlight the conditional frequencies in the table (relative frequencies in the body of the table).
b. What is the probability of randomly choosing a person with food at a baseball game and that person
being a child who prefers hamburgers?
c. What is the probability of randomly choosing a person with food at a baseball game and that person
being a teenager who prefers pizza?
d. What is the probability of randomly choosing a person with food at a baseball game and that person
being an adult who prefers pizza?
e. What percentage of the people that Carla asked were adults?
f. What percentage of the people that Carla asked were children?
g. What is the probability that a person will choose a hamburger at a baseball game?
h. What is the probability that a person will choose pizza at a baseball game?
i. What food is a person most likely to choose at a baseball game?
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286
(6-8) Two-Way Frequency Tables
(6-8)
Homework
Martin surveyed 60 of his classmates about their participation in school activities as well as whether they have a
part-time job. The results are shown in the two-way frequency table below. Use the table to complete the
exercises.
Clubs only
Works
12
Doesn’t
3
Work
Total
Sports only Both Neither Total
13
16
4
5
5
2
14.
1. Complete the table by finding the marginal frequencies and the grand total.
15.
2. Highlight the joint frequencies.
16.
3. Make a relative frequency table for the rows and the columns.
Works
Doesn’t
Work
Total
a.
b.
c.
d.
e.
f.
g.
h.
Relative Frequency of Rows
Clubs Sports Both Neither Total
only only
Works
Doesn’t
Work
Total
Relative Frequency of Columns
Clubs Sports Both Neither
only
only
Total
What percentage of working students are only in clubs?
What percentage of working students are neither in clubs nor sports?
What percentage of non-working students are in both clubs and sports?
What is the probability that a non-working student is only involved in sports?
What percentage of clubs-only students work?
What is the probability of a student being in both clubs and sports while working?
What percentage of all students participate only in sports?
What is the probability of randomly selecting a student that does not participate in any school activity?
17. 4. Make a relative frequency table by calculating the relative frequency of the marginal and joint
frequencies compared to the grand total. Write your relative frequencies as decimals and percentages.
Works
Doesn’t
Work
Total
Clubs only
Sports only
Both
Neither Total
18. 5. Highlight the conditional frequencies.
a. What is the probability of randomly selecting a student who works and is only in clubs?
b. What percentage of students who do not work are in both clubs and sports?
c. What percentage of students work?
d. What is the probability of randomly selecting a student who does neither clubs nor sports?
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287
875
73
573
81
373
381
7.1b
(refine)—More
Frequency Tables
s. Record the five
number
summary for Two-Way
(6-8) Two-Way
Frequency Tables
1
s. Record the five
summary
for that did not do their homework into two categories:
1. number
Mr. Smith
splits pupils
Record the five number
summary
first timers
and for
second(+) timers.
Med 210, Q3 248, max 289
a. Design a table to show how many boys and how many girls did not do their homework.
b. In289
one month, 36 girls and 12 boys did not do their homework for the first time. Twelve girls and 30
Med 210, Q3 248, max
ghts. Record the five number summary
boys did not do their homework for the second time. Put these figures in your table.
Med 210, Q3 248, max 289
ghts. Record the five number summary
First
Second +
Total
Girls summary36
12
48
hts. Record the five number
Boys
12
30
42
Med 80, Q3 81, max 83
Total
48
42
90
Med 80, Q3 81, max 83
he similarities and
differences?
Thetwo-way table for Hollywood Junior High’s eating habits.
2.83
Complete the
dwed
80,right.
Q3 81,The
max
weights
have a greater
he similarities and differences? The
Male
Female
Totals
wed
right. The
have The
a greater
similarities
andweights
differences?
Eat Breakfast regularly
190
110
300
ed
right.
The
weights
have
a
greater
ow adding Yao Ming willDo
change
theBreakfast
box
not Eat
regularly
130
165
295
ow adding Yao Ming will change the box
7.1a (build)—Creating
Two-Way
320Frequency Tables
275
595
Totals
w. adding
Yao
change
the did
boxthe
How did
theMing
plot will
change?
How
1. A bank teller splits transactions into two categories: deposits and withdrawals.
anges.
a. Of theHow
total did
males,
what percentage do not eat breakfast regularly? 130/320 = 41%
. How did the plot change?
the
a. Design a table
that he could use to show how many transactions are deposits and how many are
b.
Of
the
total
people
anges.
How did the plot change?withdrawals.
How did the who eat breakfast regularly, what percentage of them are males? 190/300 = 63%
ges.
b. In one shift, he has 72 transactions. Of those, 12 males make deposits and 30 make withdrawals. While
Med 80, Q3 81.5, Max 9020 females make deposits. Put these figures in your table and complete the missing portion of the table.
7.1a (build)—Creating
Frequency
Tables survey.
3. Complete
the two-way
tableTwo-Way
for Jersey
High’s
transportation
Deposits
Withdrawals
Total
Med 80, Q3 81.5, Max 90
Males
12
30Male
42Female
Totals
Med 80, Q3 81.5, Max 90
A bank teller splits
into two categories:
h is licensed under a 1. Females
20 transactions 10
30 deposits and withdrawals.
Walk
3434
46transactions80
a. Design
a table
that
he
could
use
to
show
how
many
are deposits and how many are
3.0 United States License Total
32
40
72
h is licensed under a
withdrawals.
Car
28
17
45
Unitedunder
States aLicense b. In one shift, he has 72 transactions. Of those, 12 males make deposits and 30 make withdrawals. While
s 3.0
licensed
15classes in both contemporary
12
27 hip-hop dance.
2. Heather hasBus
a dance studio that offers
and
.0 United States License
20 females make deposits. Put these figures in your table and complete the missing portion of the table.
a.
Design
a
table
that
will
show
the
number
of
female
and
male
dancers
7.1a (build)—Creating
Tables
Cycle DepositsTwo-Way
52Frequency
17
69 who take classical or hip-hop
Withdrawals
Total
classes.
Males
12 hip-hop dancers
30129and 43 male42hip-hop
92 dancers.221
Totals
She has
38splits
female
Heather has a total of 200 dancers
1. b.
AFemales
bank
teller
transactions
into
two
categories:
deposits
and withdrawals.
20 with 60 of them
10 being male.30
enrolled
in
classes
Put
these
figures
in
tableand
andhow
complete
a. Design a table32that he could use
how many
areyour
deposits
many the
are missing
40 to show
72 =transactions
a. Total
Ofportion
the
total
males,
what
percentage
cycle?
52/129
40%
of
the
table.
withdrawals.
b. c.
theone
total
people
usemale
the bus,
what
female?
12/27
many
contemporary
dancers
arepercentage
enrolled
in are
her
studio?
b.OfHow
In
shift,
he haswho
72 transactions.
Of
those,
12 males
make
deposits
and =
3044%
make withdrawals. While
2. Heather has a dance
studio
that
offers
classes
in
both
contemporary
and
hip-hop
dance.
Contemporary
Hip-hop
20 females make
deposits. Put
these figures inTotal
your table and complete the missing portion of the table.
a.
Design
a
table
that
will
show
the
number
of
female
and
male
dancers
who
take
classical or hip-hop
43
4. Malesclasses. 17
Deposits
Withdrawals 60
Total
Females
102
38
140
Males
12
30
42 hip-hop dancers. Heather has a total of 200 dancers
b.
She
has
38
female
hip-hop
dancers
and
43
male
Total
119
81
200
Females
20
10
30 Put these figures in your table and complete the missing
enrolled in classes with 60 of them being male.
Total
32table.
40
72
of the
3. Sarahportion
is worried
about how much garbage she creates each week. She decides to look at how many items
c. How many contemporary male dancers are enrolled in her studio?
she couldhas
recycle
instead
in that
threeoffers
weeks’
time.in both contemporary and hip-hop dance.
a dance
studio
classes
Contemporary
Hip-hop
Total
5. 2. a.Heather
Design
show
number
of cans,ofglass
bottles, and newspapers she recycled over the last three
a.Males
Design aa table
table17to
that
willthe
show
the
number
female
43
60 and male dancers who take classical or hip-hop
d. For each weeks.
graph,
draw
a
line
of
best
fit,
if
possible.
classes.
Females
102
140 and 4 in the last week. She recycled 6 glass bottles
3 in
second
b.
Sarah
recycled
5 cans
in thedancers
1st38week,
b.
She has
38 female
hip-hop
and
43the
male
hip-hop
dancers. Heather has a total of 200 dancers
Total
119
81
200
weeksinshe
recycled
2 and
then 3 the missing
every
week
and 1 newspaper
the last
week.
thethese
1st two
enrolled
in classes
with 60 ofin
them
being
male.InPut
figures
your
table and
complete
newspapers.
Put
these
numbers
in
your
table
and
complete
any
missing
portions.
portion
of the about
table. how much garbage she creates each week. She decides to look at how many items
is worried
Cans
Glass
Bottles
Newspapers
Total
6. 3. c.Sarah
How many contemporary male
dancers
are enrolled
in her studio?
she could
instead
in 1three
weeks’
time. School
Week
1 recycle
5Contemporary
6Hip-hop
2Total District, Utah
13 is licensed under a
Sec
Math
In-Sync
by Jordan
a. Design
a table
to show
the number
of cans, glass
bottles, and 12
newspapers
recycled
Creative
Commons
Attribution-NonCommercial-ShareAlike
3.0 Unitedshe
States
Licenseover the last three
Week
2
3
6
3
Males
43
60
17
weeks.
Week
3
4102
6 st
1 10
11
Females
week, 3 in the140
second and 4 in the last week. She recycled 6 glass bottles
b. Sarah recycled
5 cans in the 138
Total
12
18
6
36
Totalevery week and
119 1 newspaper81
in the last week.200
In the 1st two weeks she recycled 2 and then 3
newspapers. Put these numbers in your table and complete any missing portions.
3. Sarah is worried about
how much garbage
she creates
each week. She
decides to look at how many items
Bottles
Newspapers
Total
e. For the graph describeCans
how closely theGlass
points
fit the line.
she
could
recycle
instead
in
three
weeks’
time.
Week 1
5
6
2
13
Since r = 0.96 this set of data has a strong positive correlation.
(apply)—Relative, Joint, and Marginal Frequencies
(6-8) Two-Way Frequency Tables - Continued
he frequency table below shows the results of a survey that Carla took. She asked 40 randomly selected
.1c
(apply)—Analyze Frequency Tables (Joint, Marginal, and Conditional)
eople what their favorite food was to eat at a baseball game. The three choices were hotdogs, hamburgers,
pizza. Convert this
7. table into a relative frequency table that uses decimals as well as percentages.
a. 110
Copy and complete the two-way table for Hollywood Junior High’s eating habits.
Preferred Food 2.
at the
ballare
game
Hotdogs
Hamburgers
Pizza How
Total
What
the mean
and standard
deviation now?
did they change?
mean 5.05, sample
b. 275
standard
deviation
2.013,
population
standard
deviation
1.959
Female
Totals
Frequency
18 Male 12
10
40
c. 110/275 = 40%
Breakfast
regularly
190to obtain relative
110 frequencies
300as decimals. Record
Divide the numbersEat
in
the
frequency
table
by
the
total
c. Analysis: What is the relationship between the spread of the data and thed.
standard
595 deviation? The
Dobelow.
not Eat Breakfast
the results in the table
more spread out the data is the greater the standard deviation.
e. 130
295
Preferred Food at theregularly
ball game
Hotdogs 130 Hamburgers 165
Pizza
Total
320 12/40=0.30 275
Relative Frequency Totals
18/40=0.45
10/40=0.25 595
40/40=1 f. 295
g. 130/295 =
a) How many females “eat breakfast regularly”? (a joint frequency) 110
Write
the
decimals
as
percentages
in
the
table
below.
b) How many females were included in the survey? (a marginal frequency) 275
h. males
c) How many
females
eat breakfast
outgame
of the total
number of Hamburgers
females? (a conditional
Preferred
Food
at the ball
Hotdogs
Pizza relative
Total frequency) 110/275 =
i. males
8. Frequency
a) a
40% Relative
45%
30%
25%
100%
d) How many peopleb)
were
included in this survey? (this is a marginal frequency) 595
j. females
dance
e)
How
many
males
“do
not
eat
breakfast
regularly”?
(this
is
a
joint
frequency)
130
How can you check to see if you have accurately converted frequencies to relative frequencies? They
f) How many malesc)
andsports
females do not eat breakfast regularly? (this is a marginal frequency) 295
add
to
1
g) How many males
eat breakfast
of the total
number
of people
10. doa)not
12/40
= 0.3 out
; 10/40
= .25
; 40/40
= 1who do not eat breakfast?130/295 = 44%
(a conditional relative frequency)
Explain why the number
in the
total column
of a relative frequency table is always 1 or 100%? Because
; 25%
; 100%
h) Do more females b)
eat 30%
breakfast
or do more
males eat breakfast? (a comparison of joint frequencies) males
i)
group
of people
eat breakfast
c)
add
tomore
1 regularly?
the Which
margins
contain
theThey
totals
and the
total
is 1 wholemales
or 100%
j) Which group of people does not eat breakfast regularly? females
the
margins
contain
theatSchool
Sec
Math
1 In-Sync
byto
Jordan
District,
Utah isMost
licensed
under
a
What does the data d)
tell Because
us about the
most
preferred
food
eat
a baseball
game?
people
prefer
44%
Creative Commons
Attribution-NonCommercial-ShareAlike
3.0 United States License
hotdogs
totalsmen’s
& the
is 1preferences
whole
or of
100%
Below
is a table showing
andtotal
women’s
activities.
25
or her survey, Carla also
the ageprefer
of each hotdogs.
person. The results are shown in the two-way frequency
e) recorded
Most
people
a)
Looking
at
just
the
total
columns
(marginal
frequencies),
ble below. Each entry is the frequency of people who prefer a certain food and
are in aSports
certain ageTV
group. TOTAL
Dance
what can we11.
conclude about the activities?
a. Dance is more interesting.
Hotdogs
Hamburgers Pizza
Total
2
10
8
20
Men
b. They have roughly equal appeal.
Child
8
1
2
11
c. Sports is the least chosen activity.
6
8
30
Women
Teenager
5
3
5
13 16
d. TV is the preferred
activity.
8
3
16
b) Looking at the joint Adult
frequencies,5we see that women
16
16
50
TOTAL
18 activity? dance
12
10
40 18
Totalfor which
show a strong preference
c)
at themarginal
joint frequencies,
thatinmen
Fill Looking
in the missing
frequencies we
(thesee
entries
the show
total row and total column).
d) Table
in activity?
numbersports
1
a strong preference
for which
Highlight the joint frequencies (entries in the body of the table).
TheHigh’s
number
of peoplesurvey
surveyed
Below is a table for e)
Jersey
transportation
results.
Find the grand total, which is the sum of the row totals as well as the sum of the column totals. Write the grand
f) Children prefer
hotdogs
Male
Female
Totals
total in the lower-rightg)corner
of theprefer
table (the
intersection of the total column and the total row).
Adults
hamburgers
Walk
34
46rows and columns
80
3. Make a relative frequency table for the
Where have you seenh)
thehotdogs
numbers in the total row before? Table in number 1
Car
28
17
45
In terms of Carla's
survey, what
does theFrequency
grand totalofrepresent?
Relative
Rows The number of people surveyed
Relative Frequency of Columns
Bus12.
15
12
27
3.
1 of food1.5
2.5 game? Children
4
4.5 hotdogs 5
What does the
data tell us aboutx the preference
for17
children2 at a baseball
prefer
Cycle
52Hamburgers
69
Hotdogs
Pizza
Hotdogs
Hamburgers
Total
2
3
4
5
8
9
10 Pizza
y
How does this
compare
to
adults?
Adults
prefer
hamburgers
129
92
221
Totals
Child b. 0.73
0.09
0.18
1
0.44
0.08
0.2
d.Child
Teenager
0.385would0.23
1 hotdogsTeenager 0.28
0.25
0.5
Amongst all age groups
what food
you say is most0.385
preferred?
Adult
0.31
0.5
0.19
1
Adult
0.28
0.67
0.3
a) Identify one joint frequency from this table and describe its meaning. Answers will vary
0.45
0.3 this table 0.25
1
1
1
Total
Total Answers
b) Identify one marginal
frequency
from
and describe
its meaning.
will 1vary
c) Identify one conditional relative frequency from this table and describe its meaning. Answers will vary
0.18
a.a)
What
is
the
probability
a child
choose
pizza?Answers
0.18
d) Write two conclusions
you
can
makethat
from
this will
frequency
table.
Sec
Math
1that
In-Sync
by
Jordan
School
District,
Utah
is licensed
under a will vary
Total
0.28
0.32
0.4
1
b.b)
What
the probability that an adult will choose
a hamburger?
0.5
Creative
Commons
3.0 United
States License
0.5 is Attribution-NonCommercial-ShareAlike
c. What percentage of adults prefer
12 hotdogs? 31%
c)
31%
d. Sec
What
percentage
prefer
pizza?Utah
38.5%
Math
1 In-Sync of
by teenagers
Jordan School
District,
is licensed under a
Creative
Commons Attribution-NonCommercial-ShareAlike 3.0 United States License
d) 38.5%
1
e. strong
positive
correlation
4. Makec.a relative
frequency table by 11
calculating the relative
frequency
of the
marginal and joint frequencies
4.
4 frequencies
5 as decimals
7
8
10
compared to
and percentages.
x the grand1total. Write3 your relative
9
8
6
5.5
6
3
2
y
Hotdogs
Hamburger
Pizza
Total
b.
d.
b. What is the probability that an adult will choose a hamburger? 0.5
c. What percentage of adults prefer hotdogs? 31%
d. What percentage of teenagers prefer pizza? 38.5%
4. Make a relative frequency table by
calculating
the relative
frequency of
the marginal
and joint frequencies
(6-8)
Two-Way
Frequency
Tables
- Continued
Homework
compared to the grand total. Write your relative frequencies as decimals and percentages.
Martin surveyed 60 of his classmates about their participation in school activities as well as whether they
13.
part-time job. The results are shown in the two-way frequency table below. Use the table to complete the
Hotdogs
Hamburger Pizza
Total
exercises.
Child
0.2; 20%
0.025; 2.5% 0.05; 5%
0.275; 27.5%
Teenager 0.125; 12.5% 0.075; 7.5% 0.125;
Clubs12.5%
only 0.325;
Sports 32.5%
only Both Neither Total
Adult
0.125; 2.5%
0.2; 20%
0.075;
7.5%
0.4;
40%
Works
12
13
16
4
45
0.45; 45%
0.3; 30%
0.25;
25%
1;
100%
Total
Doesn’t
3
5
5
2
15
Work
b)
0.025
a. Highlight the conditional frequencies in the tableTotal
(relative frequencies
in the body
table). 6
15
18 of the21
60
Homework
c) 0.125
b. WhatMartin
is the surveyed
probability
choosing
a person
with food atina school
baseballactivities
game and
60ofofrandomly
his classmates
about
their participation
as that
wellperson
as whether they have a
d)job.
0.075
part-time
The
results
are
shown
in
the
two-way
frequency
table
below.
Use
the
table
to total.
complete the
1. hamburgers?
Complete the0.025
table by finding the marginal frequencies and the grand
being a child who prefers
e)
40%
exercises.
2. Highlight the joint frequencies.
c. What is the f)
probability
of Make
randomly
choosing
a person
withforfood
a baseball
and that person
27.5% 3.
a relative
frequency
table
the at
rows
and thegame
columns.
Homework
Clubs only Sports only Both Neither Total
being surveyed
a teenager
who
prefers
pizza? about
0.125
g) 30%
Martin
60
of his
classmates
their
participation
in school activities as well as Relative
whether they
have a of Columns
Frequency
of13
Rows
Frequency
WorksRelative 12
16
4
45
25%
job.h)
The
resultsofare
shown inchoosing
the two-way
frequency
tableatbelow.
Usegame
the table
to
complete
the
d. part-time
What is the
probability
randomly
a
person
with
food
a
baseball
and
that
person
Doesn’tClubs Sports Both Neither Total
3
5
5
2
15 Clubs Sports Both Neither
exercises. i) hotdogs
Work
only
only
only
only
being an adult who prefers pizza? 0.075
15
180.09
211
6 Works60 0.8
WorksTotal
0.27only
0.29
0.36
0.72
0.76 0.67
Sports
only 40%
Both Neither
Total
e. What percentage of the people
thatClubs
Carla
asked
were
adults?
Doesn’t
Doesn’t
Worksthat Carla
12asked
13
16
45
0.2
0.33
0.33 0.13
14
0.2
0.28
0.24 0.33
f. What 1.
percentage
of
the
people
were
children?
27.5%
Work
Work
Complete the table
by finding the marginal frequencies and the grand total.
Doesn’t
3 choose
50.35 0.1
0.25
0.3 a hamburger
1 2 game?15
1
1
1
1
Total
Total
the joint
frequencies.
g. What 2.
is Highlight
the probability
that
a person will
at 5a baseball
30%
Work
a. Whattable
percentage
working
students
are only
in clubs?
3. Make a relative frequency
the of
rows
and
columns.
15for
18at athe
21 game?
6 25%
60 27%
Total
h. What is the probability that
will
chooseofpizza
baseball
b.a person
What percentage
working
students
are neither
in clubs nor sports? 9%
Whattopercentage
non-working
in bothFrequency
clubs and sports?
33%
Relative
of Rows
Relative
of Columns
i. What food is a person
mostc.Frequency
likely
choose
at aofbaseball
game?students
hotdogsare
1. Complete the table by finding
theismarginal
frequencies
and
the grand total.
d.
What
the
probability
that
a
non-working
student
is
only
involved
in
sports?
Clubs Sports Both Neither Total
Clubs Sports Both Neither 33%
Total
2. Highlight the joint frequencies.
What percentage of clubs-only students work?
80% only
only e.only
only
3. Make a relative frequency
table
the rows and theofcolumns.
Whatfor
is
being in 0.8
both clubs
and sports
36%
Works
0.27 f.0.29
0.36 probability
0.09
1 a student
Works
0.72
0.76 while
0.67working?
0.75
g.
What
percentage
of
all
students
participate
only
in
sports?
30%
Doesn’t
Doesn’t
Relative0.2
Frequency
of is
Rows
Relative
Columns
0.33
0.13
1of randomly selecting
0.2
0.28
0.24not participate
0.33
0.25
h.0.33
What
the probability
aFrequency
student
thatofdoes
in any school act
Work
Work
10%
Sports0.3Both 0.35
Neither
0.1 Total 1
1 Total 1
Total Clubs0.25
TotalClubs1 Sports1 Both 1 Neither
only only
only
only
a. What percentage of working students are only in clubs? 27%
MakebyaJordan
relative
frequency
table
by calculating
thearelative
frequency of the
marginal and joint
a)0.27
27%
Works 16.
0.2914.In-Sync
0.09
1 are
Works
0.8
0.72
0.75
Sec
Math
School
District,
Utah
licensed
under
b. What
percentage
of0.36
working
students
neither
in is
clubs
nor sports?
9% 0.76 0.67
frequencies compared to theDoesn’t
grand3.0total.
Write
relative frequencies as decimals and percenta
Creative
Commons Attribution-NonCommercial-ShareAlike
United
Statesyour
License
Doesn’tc. b)
9%percentage
What
non-working
students
are in both clubs
0.2
0.33 of0.33
0.13
113
0.2 and sports?
0.28 33%
0.24 0.33
0.25
Work d. What is the probability that a non-working student
Workis only involved in sports? 33%
c) 33%
17.
only
0.25percentage
0.3
0.35
0.1
1 Clubs
1 only 1 Both 1
1Neither 1 Total
Total e. What
Total
of
clubs-only
students
work?
80% Sports
d)
33%
0.2;in20%
0.22;
0.27;working?
27%
0.07;
0.75; 75%
a. What
percentage
working students
are only
27%
f. What
is the of
probability
of aWorks
student
being
inclubs?
both clubs
and22%
sports while
36% 7%
e)
80%
b. What
percentage
of working
are
neither
in clubs
nor
sports?
Doesn’t
0.05; 5%
0.08;
8%
0.03; 3%
0.25; 25%
g. What
percentage
of all students
students
participate
only
in sports?
30% 9% 0.08; 8%
c. What
percentage
of
non-working
students
are
in
both
clubs
and
sports?
33%
Work
h. f)
What
is the probability of randomly selecting a student that does not participate in any school activity?
36%
d. What 10%
is the probability that a non-working
student
is only 0.3;
involved
0.25; 25%
30% in sports?
0.35;33%
35%
0.1; 10%
1; 100%
Total
g) 30%
e. What percentage of clubs-only students work? 80%
5. of
Highlight
thebeing
conditional
10%
f. What
is the
probability
a student
in both frequencies.
clubs
sportsfrequency
while working?
36%
4. h)
Make
a relative frequency
table
by calculating
theand
relative
of the marginal
and joint
a.
What
is
the
probability
of
randomly
selecting
a
student
who works and is only in clubs? 20%
g. What frequencies
percentage of
all
students
participate
only
in
sports?
30%
compared to the grand total. Write your relative frequencies as decimals and percentages.
b. randomly
What percentage
whodoes
do not
are in in
both
andactivity?
sports? 8%
h. What is the probability of
selectingofa students
student that
notwork
participate
anyclubs
school
c. What
percentage
18.
a) 20%of students work? 75%
10%
Sports onlyof randomly
Both selecting
Neither
d.Clubs
Whatonly
is b)8%
the probability
a student Total
who does neither clubs nor sports? 10
Works 0.2; 20%
0.22; 22%
0.27; 27%
0.07; 7%
0.75; 75%
4. Make a relative frequency table by calculating
the relative frequency of the marginal and joint
c) 75%
Doesn’tto the
0.05;
5% total.
0.08;
0.08;frequencies
8%
0.03;
3%
0.25;
frequencies compared
grand
Write8%
your relative
as decimals
and 25%
percentages.
Work
d) 10%
Sec Math 1 In-Sync by Jordan School District, Utah is licensed under a
0.25; 25% Creative
0.3;Commons
30% Attribution-NonCommercial-ShareAlike
0.35; 35%
0.1; 10%
1; 100%
3.0 United States License
Total
Clubs only
Sports only Both
Neither14 Total
5. Highlight
conditional
Worksthe 0.2;
20% frequencies.
0.22; 22%
0.27; 27%
0.07; 7%
0.75; 75%
a. Doesn’t
What is the
probability
of0.08;
randomly
a student0.03;
who 3%
works and
only in clubs? 20%
0.05;
5%
8% selecting
0.08; 8%
0.25;is 25%
b. Work
What percentage of students who do not work are in both clubs and sports? 8%
c. Total
What percentage
of students
0.25; 25%
0.3; work?
30% 75%0.35; 35%
0.1; 10%
1; 100%