8SP4 Essential Question How can you construct and interpret twoway frequency tables Common Core Standard 8SP Investigate patterns of association in bivariate data 4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequenci ID: 589728
Download Presentation The PPT/PDF document "Two-Way Frequency Tables" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Two-Way Frequency Tables
8.SP.4
Essential Question
?
How can you construct and interpret two-way frequency tables?Slide2
Common Core Standard:
8.SP ─ Investigate patterns of association in bivariate data
.
4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?Slide3
Objectives:
To
construct and interpret two-way frequency tables.Slide4
Curriculum Vocabulary
Conditional Relative Frequency
(
frecuencia
relativa
condicional
):
The ratio of a joint relative frequency to a related marginal relative frequency in a two-way table.
Frequency (frecuencia):
The number of times the value appears in the data set.
Joint Relative Frequency (frecuencia relativa conjunta):
The ratio of the frequency in a particular category divided by the total number of data values.
Marginal Relative Frequency (frecuencia relativa marginal):
The
sum of the
joint relative
frequencies in a row or column of
a two-way table.Slide5
Curriculum Vocabulary
Relative Frequency
(
frecuencia
relativa
)
:
The frequency of a specific data value divided by the total number of data values in the set.
Two-way Table
(de dos vías mesa):
A table that displays two-variable data by organizing it into rows and columns.
Two-way Relative Frequency Table (dos vías tabla de frecuencias
relativas):
A two-way table that displays relative frequencies.Slide6
Two-Way Frequency Tables
The
FREQUENCY
of an event is the
number of times
the event occurs.
A
TWO-WAY TABLE
shows the frequenciesof data that is categorized two ways.The rows indicate one categorizationand the columns indicate another.Slide7
Making a Two-Way Table
A poll of 120 town residents found that 40% own a bike
. Of
those who own a bike, 75% shop at the farmer’s market
. Of
those
who do not own a bike, 25% shop at the farmer’s market.
STEP 1:
Start in the bottom right cell of the table. Enter the total number of people polled.
STEP 2: Fill in the right column.
40% of 120 people own a bike.
STEP
3: Fill in the top row.75% of those who own a bike also shop at the market.(the remaining bike owners do
not shop at the market)
Farmer’sMarket
No Farmer’s Market
TOTAL
Bike
No Bike
TOTAL
120
48
72
36
12Slide8
Making a Two-Way Table
A poll of 120 town residents found that 40% own a bike
. Of
those who own a bike, 75% shop at the farmer’s market.
Of those
who do not own a bike, 25% shop at the farmer’s market.
STEP 4: Fill in the second row.
25%
of those who
do not own
a bike
shop
at the market.(the remaining people without bikes do not shop at the market)
STEP 5: Fill in the last row.I
n each column, add the numbers in the first two rows to find the total number of people in each category.
Farmer’s
Market
No Farmer’s Market
TOTAL
Bike
No Bike
TOTAL
120
48
72
36
12
18
54
54
66
How can you check that your table is completed correctly?Slide9
Deciding Whether There is Association?
RELATIVE FREQUENCY
is the RATIO of the number of times an event occurs to the total number of
events
.
Farmer’s
Market
No Farmer’s Market
TOTAL
Bike
No Bike
TOTAL
120
48
72
36
12
18
54
54
66
In the last example, the relative frequency of bike owners who shop at the farmer’s market is
You can use
RELATIVE FREQUENCIES
to decide if there is an association between two variables or events.Slide10
Deciding Whether There is Association?
Determine whether there is a association between the events
.
Curfew
No Curfew
TOTAL
Chores
16
4
20
No
Chores
16
64
80
TOTAL
32
68
100
STEP 1
:
Find the relative frequency of having to do chores.
STEP 2:
Find the relative frequency of having to do
chores among those who have a curfew.
One hundred teens were polled about whether they are required to
do chores
and whether they have a curfew. Is there an association
between having
a curfew and having to do chores?Slide11
Deciding Whether There is Association?
Determine whether there is a association between the events
.
Curfew
No Curfew
TOTAL
Chores
16
4
20
No
Chores
16
64
80
TOTAL
32
68
100
Relative frequency of having to do chores:
Relative
frequency of having to do
chores among those who have a curfew:
STEP
3: Compare the
relative
frequencies.
Students who have
a curfeware more likely to have to do chores than the general population.There IS an association.The relative frequencies show that students who have acurfew are more likely to have to do chores than the general population of teens polled in the survey.
One hundred teens were polled about whether they are required to
do chores
and whether they have a curfew. Is there an association
between having
a curfew and having to do chores?Slide12
Deciding Whether There is Association?
Determine whether there is a association between the events
.
Late
Not Late
TOTAL
Domestic
30
120
150
International
10
40
50
TOTAL
40
160
200
STEP 1
:
Find the relative frequency of a flight being late.
STEP 2:
Find the relative frequency of
a flight being late among international flights.
Data from 200 flights were collected. The flights were categorized
as domestic
or international and late or not late. Is there an
association between
international flights and a flight being late?Slide13
Deciding Whether There is Association?
Determine whether there is a association between the events
.
Late
Not Late
TOTAL
Domestic
30
120
150
International
10
40
50
TOTAL
40
160
200
Data from 200 flights were collected. The flights were categorized
as domestic
or international and late or not late. Is there an
association between
international flights and a flight being late?
Relative frequency
of
a
flight being late:
Relative
frequency of
a flight being late among international flights:
STEP 3: Compare the
relative frequencies.International flights
are no more likely
to
be late than flights in general
.
There
is
NO association.
The
relative frequencies show that
international flights
are
just as likely to be late as any other flight.
Slide14
Data from 200 middle school and high school students were collected
. Students were asked whether or not they had visited at least one national park. Is there an association
between being a high school student
and visiting
a national park?
Explain.
Have Visited a
National Park
Have NOT Visited
a National Park
TOTAL
Middle School
25
55
80
High School
80
40
120
TOTAL
105
95
200Slide15
In a survey of 50 students, 60% said that they have a cat
. Of the students who have a cat, 70% also have a dog. Of the students who do not have
a cat
, 75% have a dog
. Complete
the two-way
table.
Dog
No Dog
TOTAL
Cat
No
Cat
TOTALSlide16
The table gives partial information on the
number of men and women who play in the four sections of the Metro Orchestra.
Strings
Brass
Woodwinds
Percussion
TOTAL
Men
Women
TOTAL
Complete the table.
Is there an association between being a woman and playing strings?