From the records at TAB, the following data was collected:
12 students studied Sociology, Economics and Accounting
27 studied Sociology and Accounting
20 studied Sociology and Economics
21 studied Economics and Accounting
36 studied Sociology
36 studied Economics
58 studied Accounting
a) What is the least number of individual student records that were examined?
b) How many students studied Sociology but neither of the Business subjects
I ended up getting that 74 were examined but I don't know how to do b
all 3 = 12
s + e = 20 - 12 = 8
s + a = 27 - 12 = 15
a + e = 21 - 12 = 9
s = 36 - 12 - 8 -15 = 1
e = 36 - 12 - 8 - 9 = 7
a = 58 - 12 - 15 -9 = 22
12 + 8 + 15 + 9 + 1 + 7 + 22 = 74
as usual, for a 3-part Venn diagram,
36+36+58 - (27+20+21) + 12 = 74
To determine the least number of individual student records that were examined, we need to find the maximum number of students in any one subject. In this case, the subject with the highest number of students is Accounting, with 58 students.
Therefore, the least number of student records examined is 58.
To find the number of students who studied Sociology but neither of the Business subjects, we need to subtract the number of students who studied Sociology and at least one Business subject from the total number of students who studied Sociology.
Let's calculate this step-by-step.
1. Number of students who studied Sociology and Accounting: 27
2. Number of students who studied Sociology and Economics: 20
3. Number of students who studied all three subjects (Sociology, Economics, and Accounting): 12
To find the number of students who studied Sociology but neither of the Business subjects, we need to subtract the students who studied Sociology and at least one Business subject from the total number of students who studied Sociology.
Number of students who studied Sociology: 36
Number of students who studied Sociology and at least one Business subject: 27 + 12 = 39
Therefore, the number of students who studied Sociology but neither of the Business subjects is:
36 - 39 = -3
It seems that there might be an error in the given data or calculations because the result is negative. Please review the data and calculations to ensure accuracy.
To answer question B, we need to find the number of students who studied Sociology but neither of the Business subjects (Economics and Accounting).
To do this, we can use the principle of inclusion-exclusion. We start by adding up the number of students who studied Sociology, Economics, and Accounting, which is 12.
Next, we need to subtract the students who studied Sociology and Accounting (27) and those who studied Sociology and Economics (20), since they are counted twice in the first calculation.
Finally, we add the number of students who studied only Sociology, as they are not included in any of the previous calculations. This is found by subtracting the total number of students who studied Economics and Accounting (21) and those who studied Economics and Sociology (20) from the total number of students who studied Economics (36).
So, to calculate the number of students who studied Sociology but neither of the Business subjects:
12 - 27 - 20 + (36 - 21 - 20) = 12 - 27 - 20 + 15 = -20
Since you cannot have a negative number of students, it means that there was an error in one of the numbers you provided.
Regarding question A, to find the least number of individual student records examined, we can add up the maximum number of students in each subject.
The maximum number of students studied Sociology, Economics, and Accounting (12). Additionally, there were 36 students who studied Sociology, 36 students who studied Economics, and 58 students who studied Accounting.
Adding these numbers together:
12 + 36 + 36 + 58 = 142
Therefore, the least number of individual student records examined is 142.