Start by constructing an empty table with the appropriate column and row headers. Then use the given information to find the missing frequencies.
Likes
Dislikes
Total
Teenagers
96
4
100
Adults
21
79
100
Senior Citizens
18
82
100
Total
135
165
300
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.
We are told that teenagers, adults and seniors at a mall are surveyed about whether they like the new food court. This information is enough to determine the appropriate column and row headers for our table.
Likes
Dislikes
Total
Teenagers
Adults
Senior Citizens
Total
Writing the Given Information
Each entry in the table is called a joint frequency. We are told that 96 teenagers like the new food court and 4 do not. 21 likes and 79 dislikes were collected among adults. Moreover, 18 senior citizens like the new food court and 82 dislike it. Let's write the given information in our table.
Likes
Dislikes
Total
Teenagers
96
4
Adults
21
79
Senior Citizens
18
82
Total
Finding the Marginal Frequencies
The sums of the rows and columns are called marginal frequencies. Let's calculate the sums of the rows.
Teenagers:& 96 + 4= 100
Adults:& 21 + 79= 100
Senior Citizens:& 18 + 82= 100
Now, we will calculate the sums of the columns.
Likes:& 96 + 21 + 18 = 135
Dislikes:& 4 + 79 + 82 = 165
Finally, we have two ways of calculating the grand total. We can add the number of teenagers and adults to the number of senior citizens, or we can add the number of likes to the number of dislikes. These two numbers must be the same!
Grand total
l 100+ 100 + 100 = 300 135+ 165= 300 âś“
Finally, we can complete our table!
