a Consider the two-way table that shows the results of the survey conducted at the shopping mall.
Food Court
Shoppers
Like
Dislike
Adults
21
79
Teenagers
96
4
In order to construct the frequency tables, we need to calculate the total values of all the rows in the table.
Food Court
Shoppers
Like
Dislike
Total
Adults
21
79
21+ 79=100
Teenagers
96
4
96+ 4=100
Similarly, we also need to calculate the total values of all the columns in the table.
Food Court
Shoppers
Like
Dislike
Total
Adults
21
79
100
Teenagers
96
4
100
Total
21+ 96=117
79+ 4=83
100+ 100=200
We want to use this table to construct a two-way table that shows the joint and marginal relative frequencies. To do so, we will start by dividing each joint frequency by the grand total, 200, to obtain the joint relative frequencies.
Food Court
Shoppers
Like
Dislike
Adults
21/200 =0.105
79/200 =0.395
Teenagers
96/200 =0.48
4/200 =0.02
Similarly, we will divide each marginal frequency by the grand total to obtain the marginal relative frequencies.
Food Court
Shoppers
Like
Dislike
Total
Adults
0.105
0.395
100/200 =0.5
Teenagers
0.48
0.02
100/200 =0.5
Total
117/200 =0.585
83/200 =0.415
200/200 =1
b A conditional relative frequency is the ratio of a joint relative frequency to the marginal relative frequency. Consider the two-way frequency table that we constructed in exercise A.
Food Court
Shoppers
Like
Dislike
Total
Adults
0.105
0.395
0.5
Teenagers
0.48
0.02
0.5
Total
0.585
0.415
1
We want to construct a two-way table that shows the conditional relative frequencies based on the totals of the columns. To do so, we will divide each joint relative frequency by its corresponding marginal relative frequency. Let's do it!
Food Court
Shoppers
Like
Dislike
Adults
0.105/0.585≈ 0.18
0.395/0.415≈ 0.95
Teenagers
0.48/0.585≈ 0.82
0.02/0.415≈ 0.05
In the context of this exercise, we can make the following conclusions.
Given that someone likes the food court, the conditional relative frequency that they are an adult is approximately 18 %
Given that someone likes the food court, the conditional relative frequency that they are a teenager is approximately 82 %
Given that someone does not like the food court, the conditional relative frequency that they are an adult is approximately 95 %
Given that someone does not like the food court, the conditional relative frequency that they are a teenager is approximately 5 %
