Two-Way Tables
SECONDARY 1 MATH
Two Way Table
a way to display frequencies or relative frequencies for two categorical variables
one category is represented in rows, the other category will be in columns
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Characteristic 1
Characteristic 2
Opposite of
Characteristic 1
Opposite of
Characteristic 2
Total
Total
Frequency, how often this
combination occurred
Sum of the row
Sum of the column
Grand Total of
all combinations
Joint Frequencies
Marginal Frequencies
the number of times a combination of two conditions occur
entries that make up the “body” of the table
the number of times one specific condition occurs
entries that are in the “Total” of a row or column
Survey the class to fill in the table according to which university they cheer for if BYU played Utah in a sporting match.
What percentage of the boys cheer for BYU?
What percentage of the girls cheer for Utah?
Survey the class to fill in the table according to which university they cheer for if BYU played Utah in a sporting match.
What percentage of the people that cheer for BYU are girls?
What percentage of the class are BYU fans?
What percentage of the Utah fans are boys?
Survey the class to fill in the table according to which university they cheer for if BYU played Utah in a sporting match.
Shade in the marginal frequencies, leave the joint frequencies white
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What observation can you
make about the boys?
a large majority of boys wanted soccer as the activity
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What observation can you
make about the girls?
a large majority of girls wanted a dance as the activity
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What observation can you
make about Dance?
Of the students that wanted a dance, only a small portion were boys
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What observation can you
make about Soccer?
More students preferred to hold a soccer game than a dance
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What percent of students
that wanted a soccer game
are boys?
74.07%
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What percent of students
wanting a dance are girls?
88.46%
Ronnie is in charge of determining the upcoming after school activity.
To determine the type of activity, Rashid asked several students whether they prefer to have a dance or play a game of soccer. As Ronnie collected preferences, he organized the data in the following two-way frequency table:
What percent of total students
surveyed want a dance ?
49.06%
A survey was done by the librarian and there were 45 total students who like to read books. Of those students, 12 of them like non-fiction and the rest like fiction. Four 7th Graders like non-fiction, and twenty 8th Graders like fiction.
45
12
4
20
33
8
28
13
17
What percentage of 8th graders like fiction?
71.43%
A survey was done by the librarian and there were 45 total students who like to read books. Of those students, 12 of them like non-fiction and the rest like fiction. Four 7th Graders like non-fiction, and twenty 8th Graders like fiction.
45
12
4
20
33
8
28
13
17
What percentage of people that like nonfiction are in 7th grade?
33.33%
A survey was done by the librarian and there were 45 total students who like to read books. Of those students, 12 of them like non-fiction and the rest like fiction. Four 7th Graders like non-fiction, and twenty 8th Graders like fiction.
45
12
4
20
33
8
28
13
17
What percentage of all the people like fiction?
73.33%
Shade in the marginal frequencies,
leave the joint frequencies white
Divide the class according to whether their birthdays are in the first half of the year or last half, and whether they have brown eyes.
Jan-June
July-Dec
Brown Eyes
Not Brown Eyes
What percentage of the class has a birthday from January to June?
What percentage of the brown eyed students have later birth months?
Divide the class according to whether their birthdays are in the first half of the year or last half, and whether they have brown eyes.
Jan-June
July-Dec
Brown Eyes
Not Brown Eyes
Shade the marginal frequencies, leave the joint frequencies white
What percentage of all students were born from July to December and do not have brown eyes?
The Venn diagram compares 15 roller coasters at an amusement park as to whether or not they are made of steel and whether or not they have loops.
Made of Steel
Not Steel
Total
Has Loops
No Loops
Total
2
4
6
10
8
15
3
3
5
7
What percent of total roller coasters are steel?
53.33%
The Venn diagram compares 15 roller coasters at an amusement park as to whether or not they are made of steel and whether or not they have loops.
Made of Steel
Not Steel
Total
Has Loops
No Loops
Total
2
4
6
10
8
15
3
3
5
7
What percent of roller coasters that have loops are not steel?
40%
The Venn diagram compares 15 roller coasters at an amusement park as to whether or not they are made of steel and whether or not they have loops.
Made of Steel
Not Steel
Total
Has Loops
No Loops
Total
2
4
6
10
8
15
3
3
5
7
What percent of roller coasters that are steel also have loops?
75%
The Venn diagram compares 15 roller coasters at an amusement park as to whether or not they are made of steel and whether or not they have loops.
Made of Steel
Not Steel
Total
Has Loops
No Loops
Total
2
4
6
10
8
15
3
3
5
7
What percent of roller coasters are neither made of steel nor have loops?
20%