Question
The consistency of a drink machine is being tested. The machine dispenses the following ounces of water in five different trials: 12, 11, 10, 11, 14. What is the Interquartile Range (IQR) of the dispensing trials?(1 point) please select one of the following responses
Responses
2.5
2.5
4
4
10.5
10.5
13
Responses
2.5
2.5
4
4
10.5
10.5
13
Answers
GPT-4o mini
To calculate the Interquartile Range (IQR) of the dispensing trials, we first need to organize the data in ascending order:
The data is: 12, 11, 10, 11, 14
First, we sort it:
10, 11, 11, 12, 14
Next, we find the quartiles:
- The median (Q2) is the middle value, which is the third value in this sorted list. This value is 11.
- To find the first quartile (Q1), we take the median of the first half of the data (10, 11). The median of these two numbers is \( (10 + 11) / 2 = 10.5 \).
- To find the third quartile (Q3), we take the median of the second half of the data (12, 14). The median of these two numbers is \( (12 + 14) / 2 = 13 \).
Now, we compute the IQR:
\[ \text{IQR} = Q3 - Q1 = 13 - 10.5 = 2.5 \]
Therefore, the Interquartile Range (IQR) of the dispensing trials is 2.5.
**The correct response is: 2.5**
The data is: 12, 11, 10, 11, 14
First, we sort it:
10, 11, 11, 12, 14
Next, we find the quartiles:
- The median (Q2) is the middle value, which is the third value in this sorted list. This value is 11.
- To find the first quartile (Q1), we take the median of the first half of the data (10, 11). The median of these two numbers is \( (10 + 11) / 2 = 10.5 \).
- To find the third quartile (Q3), we take the median of the second half of the data (12, 14). The median of these two numbers is \( (12 + 14) / 2 = 13 \).
Now, we compute the IQR:
\[ \text{IQR} = Q3 - Q1 = 13 - 10.5 = 2.5 \]
Therefore, the Interquartile Range (IQR) of the dispensing trials is 2.5.
**The correct response is: 2.5**