Question

the two - way relative frequency table given shows the results from the lunch orders from an upperclassman picnic.

	11th grade	12th grade	total
sandwich	20%	24%	44%
soup	8%	30%	38%
total	40%	60%	100%

a segmented bar chart was created showing the lunch preference by grade. what percentage would the bar for 12th graders showing preferring sandwich?
options: 24%, 55%, 60%, 40%

Explanation:

Step1: Identify the relevant data

We need the percentage of 12th graders who prefer sandwiches. Looking at the table, for the "Sandwich" row and "12th Grade" column, the value is 24%. Wait, no, wait. Wait, the total for 11th grade is 40% and 12th is 60%, but the "Sandwich" row: 11th grade is 20%, 12th grade is 24%? Wait, no, let's check the table again. The table has rows: Salad, Sandwich, Soup, Total; columns: 11th Grade, 12th Grade, Total. For Sandwich: 11th Grade is 20%, 12th Grade is 24%? Wait, no, the total column for Sandwich is 44% (20% + 24% = 44%, which matches). But the question is about the bar for 12th graders preferring sandwich. Wait, maybe we need to find the percentage within 12th graders? Wait, no, the two - way relative frequency table: the percentages are relative to the total number of students? Wait, no, the total for 11th grade is 40% (12% + 20% + 8% = 40%), 12th grade is 60% (6% + 24% + 30% = 60%), and total is 100% (18% + 44% + 38% = 100%). Wait, the question is "What percentage would the bar for 12th graders show for preferring sandwich?". So we look at the 12th grade column and Sandwich row. The value in the table for 12th grade and Sandwich is 24%? Wait, no, the 12th grade column: Salad is 6%, Sandwich is 24%, Soup is 30%, Total is 60%. So the percentage of 12th graders who prefer sandwich is 24% of the total? Wait, no, in a two - way relative frequency table, if it's a relative frequency table based on the total number of students, then the percentage for 12th graders who prefer sandwich is 24% (since the table shows 24% in the 12th grade and Sandwich cell). Alternatively, if we consider the percentage within 12th graders: the total for 12th graders is 60% (from the Total row and 12th grade column). The number of 12th graders who prefer sandwich is 24% (of the total). So the percentage within 12th graders would be (24% / 60%)*100% = 40%? Wait, that can't be. Wait, no, let's re - examine the table.

Wait, the table:

| | 11th Grade | 12th Grade | Total |
|----------|------------|------------|-------|
| Salad | 12% | 6% | 18% |
| Sandwich | 20% | 24% | 44% |
| Soup | 8% | 30% | 38% |
| Total | 40% | 60% | 100% |

So the "12th Grade" column: the percentages are relative to the total number of students. So the number of 12th graders who prefer sandwich is 24% of the total number of students. But the bar for 12th graders' sandwich preference: if the bar chart is segmented by grade, then for 12th graders, the total of their preferences is 60% (from the Total row and 12th grade column). The percentage of 12th graders who prefer sandwich is (24% / 60%)*100% = 40%? Wait, no, that's not right. Wait, no, in a two - way relative frequency table, when we talk about the bar for 12th graders, we are looking at the distribution within 12th graders. So the total for 12th graders is 60% (of the total number of students). The number of 12th graders who like sandwich is 24% (of the total number of students). So the percentage within 12th graders is (24 / 60)*100 = 40%? Wait, but that contradicts the table. Wait, no, maybe the table is a joint relative frequency table (relative to the total). So to find the percentage of 12th graders who prefer sandwich, we can use the formula:

Percentage of 12th graders who prefer sandwich = (Number of 12th graders who prefer sandwich / Total number of 12th graders)*100

Number of 12th graders who prefer sandwich (as a percentage of total) = 24%

Total number of 12th graders (as a percentage of total) = 60%

So (24 / 60)*100 = 40%? But that's not one of the options? Wait, the options are 24%, 55%, 60%, 40%. Wait, maybe I made a mistake. Wait, the question is "What percentage would the bar for 12th graders show for preferring sandwich?". If the bar chart is a segmented bar chart showing the distribution within each grade, then for 12th graders, the total of their lunch preferences is 100% (within 12th graders). So we need to find the relative frequency within 12th graders.

The number of 12th graders who prefer salad: 6% of total, soup: 30% of total, sandwich: 24% of total.

Total number of 12th graders: 6% + 24% + 30% = 60% of total.

So the percentage of 12th graders who prefer sandwich is (24% / 60%)*100% = 40%.

Step2: Confirm the calculation

We have the number of 12th graders who like sandwich as 24% (of total) and the total number of 12th graders as 60% (of total). So the ratio is 24/60 = 0.4, and 0.4*100% = 40%.

Answer:

40%