Start by filling in the two-way table with the given values.
Popcorn
No Popcorn
Total
Drink
74
15
89
No Drink
10
6
16
Total
84
21
105
Practice makes perfect
A two-way table is a frequency table that displays data collected from one source that belongs to two different categories. One category of data is represented by rows and the other is represented by columns. We want to organize the given information in a two-way table. To do so, we will follow three steps.
Construct an empty table with the appropriate column and row headers.
Fill in the table with the given values.
Find the rest of values.
Let's do these three things one at a time.
Constructing the Table
We are told that some people in the theater had popcorn and some people had a drink. This information is enough to determine the appropriate column and row headers for our table.
Popcorn
No Popcorn
Total
Drink
No Drink
Total
Filling in the Table
We are told that there were 105 people in the theater. Out of the 84 people who had popcorn, 10 did not have a drink. Moreover, 6 people had neither popcorn nor drink.
Popcorn
No Popcorn
Total
Drink
No Drink
10
6
Total
84
105
Finding the Missing Values
To calculate the number of people without a drink, we add the number of people with popcorn only to the number of people without a popcorn or drink. The number of people without popcorn is the number of people with popcorn subtracted from the total number of people in the theater.
No Drink:& 10+ 6= 16
No Popcorn:& 105- 84= 21
Let's complete the table with the new information.
Popcorn
No Popcorn
Total
Drink
No Drink
10
6
16
Total
84
21
105
Let's calculate the differences between the last row and the second row to find the missing values.
Drink and Popcorn:& 84 - 10 = 74
Drink and No Popcorn:& 21 - 6 = 15
Drink:& 105 - 16 = 89
Finally, we can complete our table!
