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
(1 point)
Responses
85
85
90
90
92.5
92.5
95
Answers
GPT-4o mini
To find the third quartile (Q3) for the given test scores, we first need to organize the data in ascending order.
The test scores arranged in ascending order are:
25, 35, 45, 50, 60, 80, 90, 95, 100
To find the third quartile (Q3), we can use the following steps:
1. **Count the number of data points**: There are 9 scores in total.
2. **Determine the position of Q3**: Q3 is the value at the 75th percentile, which can be calculated using the formula \( Q3 = \frac{3(n + 1)}{4} \), where \( n \) is the number of data points. Here, \( n = 9 \):
\[
Q3 = \frac{3(9 + 1)}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is located halfway between the 7th and 8th values in the ordered list.
3. **Identify the 7th and 8th values in the ordered list**:
- The 7th value is 90.
- The 8th value is 95.
4. **Calculate Q3**:
\[
Q3 = \frac{90 + 95}{2} = \frac{185}{2} = 92.5
\]
Thus, the value of the third quartile (Q3) for this data set is **92.5**.
The test scores arranged in ascending order are:
25, 35, 45, 50, 60, 80, 90, 95, 100
To find the third quartile (Q3), we can use the following steps:
1. **Count the number of data points**: There are 9 scores in total.
2. **Determine the position of Q3**: Q3 is the value at the 75th percentile, which can be calculated using the formula \( Q3 = \frac{3(n + 1)}{4} \), where \( n \) is the number of data points. Here, \( n = 9 \):
\[
Q3 = \frac{3(9 + 1)}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is located halfway between the 7th and 8th values in the ordered list.
3. **Identify the 7th and 8th values in the ordered list**:
- The 7th value is 90.
- The 8th value is 95.
4. **Calculate Q3**:
\[
Q3 = \frac{90 + 95}{2} = \frac{185}{2} = 92.5
\]
Thus, the value of the third quartile (Q3) for this data set is **92.5**.