Question
The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90. What is the value of the third quartile for this data set? (1 point) Responses 85 85 90 90 92.5 92.5 95
Answers
GPT-4o mini
To find the third quartile (Q3) of the data set, we need to follow these steps:
1. **Arrange the data in ascending order**:
The scores are: 25, 35, 45, 50, 60, 80, 90, 95, 100.
2. **Determine the position of Q3**:
The third quartile is located at the \( \frac{3(n + 1)}{4} \) position, where \( n \) is the number of data points. In this case, \( n = 9 \).
\[
\text{Position of Q3} = \frac{3(9 + 1)}{4} = \frac{3 \times 10}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is halfway between the 7th and 8th values in the ordered list.
3. **Find the values at the 7th and 8th positions**:
The ordered data set is: 25, 35, 45, 50, 60, 80, 90, 95, 100.
- 7th value (position 7) = 90
- 8th value (position 8) = 95
4. **Calculate Q3**:
Since Q3 is at position 7.5, we take the average of the 7th and 8th values:
\[
Q3 = \frac{90 + 95}{2} = \frac{185}{2} = 92.5
\]
Thus, the value of the third quartile (Q3) for this data set is **92.5**.
1. **Arrange the data in ascending order**:
The scores are: 25, 35, 45, 50, 60, 80, 90, 95, 100.
2. **Determine the position of Q3**:
The third quartile is located at the \( \frac{3(n + 1)}{4} \) position, where \( n \) is the number of data points. In this case, \( n = 9 \).
\[
\text{Position of Q3} = \frac{3(9 + 1)}{4} = \frac{3 \times 10}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is halfway between the 7th and 8th values in the ordered list.
3. **Find the values at the 7th and 8th positions**:
The ordered data set is: 25, 35, 45, 50, 60, 80, 90, 95, 100.
- 7th value (position 7) = 90
- 8th value (position 8) = 95
4. **Calculate Q3**:
Since Q3 is at position 7.5, we take the average of the 7th and 8th values:
\[
Q3 = \frac{90 + 95}{2} = \frac{185}{2} = 92.5
\]
Thus, the value of the third quartile (Q3) for this data set is **92.5**.