Worksheet: Two-Way Frequency Tables

In this worksheet, we will practice constructing and using two-way tables.

Q1:

Which of the following is not true about two-way tables?

  • AThey are a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.
  • BThey describe the relationship between two categorical variables.
  • CThey organize data into classes and show the frequency of each class.
  • DThey represent a table of counts.

Q2:

Daniel wrote 20 letters and 80% had no mistakes. Mason wrote 28 letters and 75% had no mistakes. If a letter is selected at random, what is the probability that the letter has a mistake and was written by Daniel?

  • A112
  • B13
  • C34
  • D45
  • E716

Q3:

The following table represents the data collected from 200 conference attendees of different nationalities:

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man454040125
Woman15204075
Sum606080200

Find the probability that a randomly selected participant is an Arabic-speaking woman.

Q4:

The following table represents the data collected from 200 conference attendees of different nationalities:

ParticipantArabic SpeakerEnglish SpeakerFrench SpeakerTotal Sum
Man454025110
Woman20254590
Sum656570200

Find the probability that a randomly selected participant speaks both Arabic and English.

Q5:

The data about 50 students and the sports they play is shown in the table. What is the probability that a student selected at random is a female who plays basketball?

TennisBasketballSum
Male17926
Female16824
Sum331750

Q6:

The table shows the genders and nationalities of 250 people who entered a competition. One person is selected at random to win the prize. What is the probability that the winner is an Italian woman?

AttendenceItalianAustralianAmericanTotal
Man154585145
Woman603510105
Total758095250

Q7:

The data about 50 students and the sports they play is shown in the table. What is the probability that a student selected at random is female?

FootballBasketballSum
Male6511
Female172239
Sum232750

Q8:

The table shows the distribution of 49 students with respect to their gender and whether they regularly exercise or not. If a student is randomly chosen, find the probability that they do not exercise regularly.

GenderExercises RegularlyDoes Not Exercise Regularly
Male1115
Female167
  • A1549
  • B2249
  • C17
  • D114
  • E2749

Q9:

225 people have registered for a competition which will randomly select one winner. Their ages and genders are shown in the table. What is the probability that the winner is aged between 18 and 29?

18–2930–3940–4950–59
Male47121034
Female31453313
  • A4390
  • B2645
  • C1945
  • D2675

Q10:

Which of the following is not a two-way table?

  • A
    ClassABC
    Number of Failed Students102030
  • B
    MathEnglish Science
    Girls504020
    Boys653010
  • C
    Wearing YellowNot Wearing Yellow
    Girls5040
    Boys6530
  • D
    Like SkateboardsDo Not Like Skateboards
    Like Snowmobiles5040
    Do Not Like Snowmobiles6530
  • E
    WalkCycle
    Male5040
    Female6530

Q11:

Elizabeth collected data to see whether there was a relationship between the gender of students and their wearing yellow on the day of the survey. She randomly surveyed her class and the results are as shown.

GenderWearing YellowNot Wearing Yellow
Girls1010
Boys3020

What percentage of the girls were wearing yellow? Round your answer to the nearest integer, if needed.

Q12:

The two-way frequency table, shown below, displays the data collected from a random group of high-school students regarding whether they like skateboards and/or snowmobiles.

  Like SkateboardsDo Not Like Skateboards
Like Snowmobiles8025
Do Not Like Snowmobiles4510

How many students participated in the survey?

Q13:

A number of students, girls and boys, were asked to choose their favorite subject from math, English, and science. The results are shown in the given two-way relative frequency table.

MathEnglishScience
Girls504040
Boys653070

What percentage of the students chose science (approximated to the nearest integer)?

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