Start by constructing an empty table with the appropriate column and row headers. Then use the given information to find the missing frequencies.
Table:
In Favor of Planting a Community Garden
Gender
Yes
No
Total
Girls
71
17
88
Boys
61
35
96
Total
132
52
184
Interpretation of the Marginal Frequencies: 88 girls and 96 boys were surveyed. 132 students are in favor of planting a community garden and 52 are against. A total of 184 students were surveyed.
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.
Let's do these three things one at a time. Then we will interpret the marginal frequencies.
Constructing the Table
We are told that boys and girls are surveyed as to whether or not they are in favor of planting a community garden at school. This information is enough to determine the appropriate column and row headers for our table.
In Favor of Planting a Community Garden
Gender
Yes
No
Total
Girls
Boys
Total
Finding the Joint Frequencies
Each entry in the table is called a joint frequency. We are told that of the 96 boys surveyed, 61 are in favor of planting the community garden. Of the 88 girls surveyed, 17 are against the garden. With this information, we can find the number of boys that are against planting a community garden and the number of girls that are in favor.
Boys against:& 96- 61= 35
Girls in favor:& 88- 17= 71
Let's write the given and the newly obtained information in our table.
In Favor of Planting a Community Garden
Gender
Yes
No
Total
Girls
71
17
88
Boys
61
35
96
Total
Finding the Marginal Frequencies
The sums of the rows and columns are called marginal frequencies. Let's calculate these sums to find the missing marginal frequencies.
Students in favor:& 71+ 61=132
Students against:& 17+ 35=52
Finally, we have two ways of calculating the grand total. We can add the number of girls to the number of boys, or we can add the students in favor to the students against. These two numbers must be the same!
Grand total
l 88+ 96 =184 132+52=184 âś“
Finally, we can complete our table!
In Favor of Planting a Community Garden
Gender
Yes
No
Total
Girls
71
17
88
Boys
61
35
96
Total
132
52
184
Interpreting the Marginal Frequencies
In the marginal frequencies, we can see that 88 girls and 96 boys were surveyed. Moreover, 132 students are in favor of planting a community garden and 52 are against. A total of 184 students were surveyed.
