From 85 Records at D.S. Collegiate, the following data was collected: 12 studied Sociology, Economics and Accounting, 27 studied sociology and accounting, 20 studied economics and accounting, 21 studied economics and sociology, 36 studied sociology, 36 studied economics and 58 studied accounting
a) Draw a Venn Diagram to represent the situation
b) How many student records were examined?
c) How many students studied Sociology but neither the business subjects?
Draw your 3 overlapping circles.
Place 12 in the intersection of all three.
Now look at the sociology and accounting overlap, 12 are already included leaving you with 27-12 or 15 to go in the part showing only sociology and accounting overlap.
Continue in this fashion ...
Ok I did that but when I finished, I got a answer that no one took Sociology alone and 74 students records were examined. Can you please check this?
correct
a) To draw a Venn Diagram representing the situation, we can start by drawing three overlapping circles. Let's label these circles as "Sociology," "Economics," and "Accounting."
Now, we can fill in the given information. From the data, we know that 12 students studied Sociology, Economics, and Accounting, so we can place this number in the intersection of all three circles. Similarly, we know that 27 students studied Sociology and Accounting, 20 students studied Economics and Accounting, and 21 students studied Economics and Sociology. We can place these numbers in the appropriate intersections of two circles.
Next, we know that 36 students studied Sociology, 36 students studied Economics, and 58 students studied Accounting. We can place these numbers in the individual circles for each subject.
The Venn Diagram should now be complete, showing the overlapping areas and the numbers in each intersection and circle.
b) To determine how many student records were examined, we need to add up the numbers in all the areas of the Venn Diagram. This includes the numbers in all the intersections and circles.
From the given data, we can add up the following:
- Students who studied Sociology, Economics, and Accounting (12)
- Students who studied Sociology and Accounting (27)
- Students who studied Economics and Accounting (20)
- Students who studied Economics and Sociology (21)
- Students who studied Sociology only (36)
- Students who studied Economics only (36)
- Students who studied Accounting only (58)
Adding these numbers together, we get:
12 + 27 + 20 + 21 + 36 + 36 + 58 = 210
Therefore, 210 student records were examined.
c) To determine how many students studied Sociology but neither the business subjects, we need to subtract the number of students in the intersection of Sociology and either Economics or Accounting from the total number of students who studied Sociology.
From the given data, we know that:
- Students who studied Sociology and Accounting (27)
- Students who studied Sociology and Economics (21)
We can subtract these numbers from the total number of students who studied Sociology (36):
36 - (27 + 21) = 36 - 48 = -12
It appears that our calculation has resulted in a negative number, which doesn't make sense in this context. It is likely there was an error or inconsistency in the data provided.
In this case, we may not be able to determine the exact number of students who studied Sociology but neither the business subjects without further clarification or corrected data.