Q 33. - The Practice of Statistics for AP

Question

Marginal distributions aren’t the whole story Here are the row and column totals for a two-way table with two rows and two columns:

Find two different sets of counts $a, b, c,$ and $d$ for the body of the table that gives these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

Step-by-Step Solution

Answer

20	30	50			40	10	50
40	10	50			20	30	50
60	40	100			60	40	100

10	40	50			50	0	50
50	0	50			10	40	50
60	40	100			60	40	100

Step 1: Given information

The table is 

a	b	50
c	d	50
60	40	100

Step 2: Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph.  

Step 3: Explanation

Below is an alternate set of counts $a, b, c,$ and$d$ for the table's body that provides the same totals: 

a	b	50			30	20	50
c	d	50			30	20	50
60	40	100			60	40	100

20	30	50			40	10	50
40	10	50			20	30	50
60	40	100			60	40	100

10	40	50			50	0	50
50	0	50			10	40	50
60	40	100			60	40	100

This explains why the relationship between two variables cannot be determined solely by looking at the two individual variables.

As a result, the two different sets of counts have been discovered.