A two-way table is a frequency table that displays two categories of data collected from the same source. One category of data is represented by rows and the other is represented by columns. We want to find and interpret the marginal frequencies. Let's do these things one at a time.

Finding the Marginal Frequencies

We are given the following frequency table.

	Football Game
Dance	Attend	Not Attend
Attend	$35$	$5$
Not Attend	$16$	$20$

The sums of the rows and columns are called marginal frequencies. Let's calculate these sums to find the marginal frequencies.

Students attending a school dance : 35 + 5 = 40 Students not attending a school dance : 16 + 20 = 36 Students attending a football game : 35 + 16 = 51 Students not attending a football game : 5 + 20 = 25

Finally, we have two ways of calculating the grand total. We can add the number of students

attending

a

school

dance

to the number of students

not

attending

a

school

dance,

or we can add the students

attending

a

football

game

to the students

not

attending

a

football

game .

These two numbers must be the same!

\underline{Grand total} 40 + 36 = 76 51 + 25 = 76 ✓

Finally, we can complete our table!

	Football Game
Dance	Attend	Not Attend	Total
Attend	$35$	$5$	$40$
Not Attend	$16$	$20$	$36$
Total	$51$	$25$	$76$

Interpreting the Marginal Frequencies

In the marginal frequencies, we can see that $40$ students are planning to attend a school dance and $36$ students are not. Moreover, $51$ students are planning to attend a football game and $25$ are not. A total of $76$ students were surveyed.

Exercise

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