Two Way Tables and Relative Frequencies
NAME ______________________________
Math I
Part A
In the table below is the data from Mr. Austin’s ten-point quiz. Students need to score 6 or better to pass the quiz.
1. Make a two-way frequency table showing how many students passed the quiz and how many failed in each class.
2. Shade the joint frequencies in green. These are the values that represent the numbers of students that passed or
failed the quiz in each class.
3. Shade the marginal frequencies in blue. These are the values that represent the totals shown in all rows and the
totals shown in all columns.
4. If Mr. Austin wanted to see how many students passed in all three classes combined, would he look at joint frequencies
or marginal frequencies?
5. If Mr. Austin wanted to see write a ratio of passing students to the number of failing students for each class, would he
look at joint frequencies or marginal frequencies?
6. In which class period did the greatest number of students pass the test?
7. In which class period did the greatest number of students fail the test?
8. How many students are in Mr. Austin’s 1st period math?
Part B
1. Complete the table for the activities chosen by 74 teenagers on an activity field trip.
Rock Climbing
Mountain Climbing
Boys
Girls
Total
5
7
20
Total
2. There are 150 children at summer camp and 71 signed up for swimming. There are a total of 62 children that signed
up for canoeing and 28 of them also signed up for swimming.
Construct a two-way table summarizing the data.
Part C
The frequency table below shows the results of a survey that Carla took. She asked 40 randomly selected people what
their favorite food was to eat at a baseball game. The three choices were hotdogs, hamburgers, or pizza.
Preferred Food at Game
Hot Dogs
Hamburgers
Pizza
Total
18
12
10
40
Frequency
1. 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 Game
Hot Dogs
Hamburgers
Frequency
18/40=0.45
Pizza
Total
Pizza
Total
b. Write the decimals as percentages in the table below.
Preferred Food at Game
Hot Dogs
Frequency
Hamburgers
45%
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?
For her survey, Carla also recorded the age of each person. The results are shown in the two-way frequency table below.
Each entry is the frequency of people who prefer a certain food and are in a certain age group.
Hot dogs
Hamburgers
Pizza
Child
8
1
2
Teenager
5
3
5
Adult
5
8
3
Total
Total
2. a. Highlight or shade the joint frequencies (entries in the body of the table).
b. Compute the marginal frequencies and enter them into the table (the entries in the total row and total column).
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?
3. Make a relative frequency table displaying relative frequencies for each age group (for the rows). Write your relative
frequencies as decimals and percents.
Hot dogs
Hamburgers
Pizza
Total
Child
Teenager
Adult
Total
Make a relative frequency table showing relative frequencies for each food choice (for the columns). Write your
relative frequencies as decimals and percents.
Hot dogs
Hamburgers
Pizza
Total
Child
Teenager
Adult
Total
a. What percent of adults chose a hamburger?
b. What percent of children will choose pizza?
c. What percent of those that prefer hotdogs are adults?
d. What percent of those that prefer pizza are teenagers?
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 percents.
Hot dogs
Hamburgers
Pizza
Total
Child
Teenager
Adult
Total
a. Highlight or shade the conditional frequencies in the table (relative frequencies in the body of the table).
b. What percent of people with food at the baseball game were children who prefer hamburgers?
c. What percent of people with food at the baseball game were teenagers who prefer pizza?
d. What percent of people with food at the baseball game were adults who prefer pizza?
e. What percent of the people that Carla asked were adults?
f. What percent of the people that Carla asked were children that preferred pizza?
g. What percent of people surveyed chose a hamburger at the baseball game?
h. What percent of people chose pizza at the baseball game?
i. What food is a person most likely to choose at the baseball game?
Part D
Use the relative frequency table given to answer the questions.
1. A total of 200 students in two different age groups were surveyed about whether they eat breakfast of do not eat
breakfast. The results are shown in the relative frequencies table below.
Eat Breakfast
Do Not Eat Breakfast
Total
Ages 10-13
0.35
0.1
0.45
Ages 14-17
0.35
0.2
0.55
Total
0.70
0.30
1.0
a. How many students surveyed that eat breakfast are ages 14-17?
b. How many students surveyed are ages 10-13?
c.
How many students surveyed do not eat breakfast?
d. How many more students surveyed that do not eat breakfast are ages 14-17 than are ages 10-13?
e. How many more of the students 10-13 that were surveyed eat breakfast than do not eat breakfast?
2. At South High School, 400 students were surveyed regarding mode of transportation to and from school. The results
are shown in the relative frequency table below.
Walk
Bike
Car Pool
Bus
Boys
0.05
0.01
0.15
0.36
Girls
0.03
0.01
0.14
0.25
a. How many boys walk to school?
b. How many girls ride a bus to school?
c.
How many girls were surveyed?
d. How many students surveyed car pool?
e. How many more students ride the bus than walk to school?
f.
How many boys use a mode of transportation other than the bus?
g. How many girls walk or bike to school?
h. How many more boys ride the bus to school than girls?