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
21
79
100
Teenagers
96
4
100
Total
117
83
200
We want to construct a two-way table that shows the conditional relative frequencies based on the totals of the rows. To do so, we will divide each joint frequency by its corresponding row total. For our table we will not have marginal frequencies. Let's do it!
Food Court
Shoppers
Like
Dislike
Adults
21/100 =0.21
79/100 =0.79
Teenagers
96/100 =0.96
4/100 =0.04
In the context of the exercise, we can say that 21 % of the adults like the new food court and 79 % do not. Additionally, 96 % of the surveyed teenagers answered like and 4 % dislike when asked the same question.
