Two-way Tables

ID: munog-pitub
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Two-way Tables

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Problem 1

This two-way table shows the results of asking students if they prefer to have gym class in the morning or the afternoon.

morningafternoontotalgrade 615823grade 8182139grade 10122638total4555100\begin{array}{|c|c|c|c|} \hline \\[-1em] & \textbf{morning} & \textbf{afternoon} & \textbf{total} \\[-1em] \\ \hline \\[-1em] \textbf{grade 6} & 15 & 8 & 23 \\[-1em] \\ \hline \\[-1em] \textbf{grade 8} & 18 & 21 & 39 \\[-1em] \\ \hline \\[-1em] \textbf{grade 10} & 12 & 26 & 38 \\[-1em] \\ \hline \\[-1em] \textbf{total} & 45 & 55 & 100 \\[-1em] \\ \hline \end{array}

1) How many students participated in the survey?

2) How many students in grade 8 prefer to have gym in the morning?

3) How many grade 10 students participated in the survey?

4) How many students prefer to have gym in the afternoon?

Problem 2

A random sample of adults are asked about their preferences for a first dinner date with someone. Given the following information, find the values for each of the labeled cells in the table.

  • 122 people responded to the survey.
  • 50 of the people who said they order dessert said they also prefer to split the check.
  • 68 people prefer splitting the check.
  • 56 people prefer to skip dessert rather than ordering one.


order dessertno dessertsplit the checkABone person paysCD\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{order dessert} & \textbf{no dessert} \\[-1em] \\ \hline \\[-1em] \textbf{split the check} & \text{A} & \text{B} \\[-1em] \\ \hline \\[-1em] \textbf{one person pays} & \text{C} & \text{D} \\[-1em] \\ \hline \end{array}

5) Cell A

6) Cell B

7) Cell C

8) Cell D

Problem 3

9) Students in the 7th, 8th, and 9th grade were asked whether they prefer to write in pen or pencil.

  • 40 students prefer to write in pen.
  • 60 students prefer to write in pencil.


Create values that could represent the number of students in the 7th, 8th, and 9th grade that responded to the survey.

Problem 4

A recent study observed the number of bike riders ages 0 to 20 that wear helmets. The results are represented in the table.

wear helmentdid not wear helmet0-5 years2146-10 years341411-15 years141815-20 years312\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{wear helment} & \textbf{did not wear helmet} \\[-1em] \\ \hline \\[-1em] \textbf{0-5 years} & 21 & 4 \\[-1em] \\ \hline \\[-1em] \textbf{6-10 years} & 34 & 14 \\[-1em] \\ \hline \\[-1em] \textbf{11-15 years} & 14 & 18 \\[-1em] \\ \hline \\[-1em] \textbf{15-20 years} & 3 & 12 \\[-1em] \\ \hline \end{array}

10) Make an observation based on a data value that is not in the table. Explain your reasoning.