Question

A group of students was surveyed to find out if the students like fiction books and/or non-fiction books. The results of the survey are shown below:

44 students like fiction books
8 students like fiction books but do not like non-fiction books
51 students like non-fiction books
5 students do not like fiction books or non-fiction books
Four students created the tables below to represent the data. F represents fiction books, and NF represents non-fiction books.

Jake
Like F Do Not Like F Total
Like NF 36 15 51
Do Not Like NF 8 5 13
Total 44 20 64
Bella
Like F Do Not Like F Total
Like NF 8 23 31
Do Not Like NF 36 15 51
Total 44 28 64
Cate
Like F Do Not Like F Total
Like NF 23 8 29
Do Not Like NF 15 36 11
Total 38 44 82
Rob
Like F Do Not Like F Total
Like NF 5 36 51
Do Not Like NF 23 8 31
Total 28 44 72

Which student's table is correct?
Jake
Bella
Cate
Rob

Answer 1

To analyze the survey data, we need to find out how many students enjoy fiction (F) and non-fiction (NF) books, and then check each student's table against the given information:

1. Total students surveyed = 64
2. Students who do not like fiction or non-fiction = 5
3. Therefore, the students who like either fiction or non-fiction or both = 64 - 5 = 59 students.

Now, breaking it down:
- Students who like only fiction: 8 (given)
- Students who like fiction (total): 44 (given)
- Students who like non-fiction (total): 51 (given)

We can calculate the number of students who like both fiction and non-fiction using the principle of inclusion-exclusion:

Let:
- \( F \) = Total students who like fiction = 44
- \( NF \) = Total students who like non-fiction = 51
- \( B \) = Students who like both fiction and non-fiction
- Students who like only fiction = 44 - B
- Students who like only non-fiction = 51 - B

From our known data:
\[
(44 - B) + (51 - B) + B + 5 = 64
\]

This simplifies to:
\[
44 + 51 - B + 5 = 64
\]
\[
100 - B = 64
\]
\[
B = 36
\]

So:
- Students who like both fiction and non-fiction: 36
- Students who only like fiction: \( 44 - 36 = 8 \)
- Students who only like non-fiction: \( 51 - 36 = 15 \)

Now, we can summarize the student count:
- Like Fiction Only: \( 8 \)
- Like Non-Fiction Only: \( 15 \)
- Like Both: \( 36 \)
- Total who like either (or both) = \( 8 + 15 + 36 = 59 \)
- Do not like either: \( 5 \)

Now we'll analyze the tables created by each student.

1. **Jake's Table:**
- Likes Fiction & Likes Non-Fiction: 36
- Likes Fiction & Does Not Like Non-Fiction: 8
- Does Not Like Fiction & Likes Non-Fiction: 15
- Does Not Like Fiction & Does Not Like Non-Fiction: 5
- Total = 36 + 8 + 15 + 5 = 64 (Correct)

2. **Bella's Table:**
- Likes Fiction & Likes Non-Fiction: 8
- Likes Fiction & Does Not Like Non-Fiction: 23 (Incorrect, since it needs to be 36)
- Does Not Like Fiction & Likes Non-Fiction: 36
- Does Not Like Fiction & Does Not Like Non-Fiction: 15
- Total = 8 + 23 + 36 + 15 = 82 (Incorrect)

3. **Cate's Table:**
- Likes Fiction & Likes Non-Fiction: 23 (Incorrect)
- Likes Fiction & Does Not Like Non-Fiction: 15
- Does Not Like Fiction & Likes Non-Fiction: 36
- Does Not Like Fiction & Does Not Like Non-Fiction: 11 (Incorrect)
- Total = 38 + 44 = 82 (Incorrect)

4. **Rob's Table:**
- Likes Fiction & Likes Non-Fiction: 5 (Incorrect)
- Likes Fiction & Does Not Like Non-Fiction: 36
- Does Not Like Fiction & Likes Non-Fiction: 23
- Does Not Like Fiction & Does Not Like Non-Fiction: 8
- Total = 28 + 44 = 72 (Incorrect)

Therefore, only **Jake's table** correctly represents the survey data.