Question
The chart below shows the distribution of the number of books in a library.
A circle graph titled Types of Books. The largest proportion is Literature, then Fantasy, then non-fiction, then children's.
Sahira chooses a random sample from the library and records the type of books in the chart below.
Type of Book
Number
Fantasy
10
Literature
25
Children’s
4
Nonfiction
11
Which explains whether or not Sahira’s sample is representative?
No, it is not representative because literature books were chosen much more often than the other types.
Yes, it is representative because each type of book was chosen a unique number of times.
Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.
Yes, it is representative because each type of book was selected as part of the sample.
A circle graph titled Types of Books. The largest proportion is Literature, then Fantasy, then non-fiction, then children's.
Sahira chooses a random sample from the library and records the type of books in the chart below.
Type of Book
Number
Fantasy
10
Literature
25
Children’s
4
Nonfiction
11
Which explains whether or not Sahira’s sample is representative?
No, it is not representative because literature books were chosen much more often than the other types.
Yes, it is representative because each type of book was chosen a unique number of times.
Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.
Yes, it is representative because each type of book was selected as part of the sample.
Answers
GPT-4o mini
The correct explanation for whether Sahira's sample is representative or not can be derived from comparing her sample proportions to the distribution shown in the circle graph.
In the library, the largest proportion is Literature, followed by Fantasy, Non-fiction, and then Children's books. Let's break down Sahira's sample:
- Fantasy: 10
- Literature: 25
- Children's: 4
- Nonfiction: 11
To determine if her sample is representative, we should analyze if these numbers reflect the proportions of the types in the library.
1. **Calculate the total number of books in her sample:**
\(10 + 25 + 4 + 11 = 50\)
2. **Calculate the proportion of each type in the sample:**
- Proportion of Fantasy: \(10/50 = 0.20\)
- Proportion of Literature: \(25/50 = 0.50\)
- Proportion of Children's: \(4/50 = 0.08\)
- Proportion of Nonfiction: \(11/50 = 0.22\)
3. **Compare these proportions with the circle graph.** If the proportions significantly differ from what the circle graph indicates, then the sample won't be representative.
Since Literature dominates the sample (50%), and it is likely that the circle graph shows Literature as the largest portion, we cannot definitively say it's representative because we don't have the exact proportions from the graph for comparison.
However, the significant difference in how often Literature is chosen compared to the other types indicates a lack of balance in representation.
Thus, the best choice is:
**No, it is not representative because literature books were chosen much more often than the other types.**
In the library, the largest proportion is Literature, followed by Fantasy, Non-fiction, and then Children's books. Let's break down Sahira's sample:
- Fantasy: 10
- Literature: 25
- Children's: 4
- Nonfiction: 11
To determine if her sample is representative, we should analyze if these numbers reflect the proportions of the types in the library.
1. **Calculate the total number of books in her sample:**
\(10 + 25 + 4 + 11 = 50\)
2. **Calculate the proportion of each type in the sample:**
- Proportion of Fantasy: \(10/50 = 0.20\)
- Proportion of Literature: \(25/50 = 0.50\)
- Proportion of Children's: \(4/50 = 0.08\)
- Proportion of Nonfiction: \(11/50 = 0.22\)
3. **Compare these proportions with the circle graph.** If the proportions significantly differ from what the circle graph indicates, then the sample won't be representative.
Since Literature dominates the sample (50%), and it is likely that the circle graph shows Literature as the largest portion, we cannot definitively say it's representative because we don't have the exact proportions from the graph for comparison.
However, the significant difference in how often Literature is chosen compared to the other types indicates a lack of balance in representation.
Thus, the best choice is:
**No, it is not representative because literature books were chosen much more often than the other types.**