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 IQR of the dispensing trials?(1 point)
The IQR is
The IQR is
Answers
GPT-4o mini
To calculate the Interquartile Range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3) of the data set.
Given the dispensing trials: 12, 11, 10, 11, 14
1. **Sort the data:**
- The sorted data: 10, 11, 11, 12, 14
2. **Determine Q1 and Q3:**
- Q1 is the median of the first half (lower half) of the data.
- Q3 is the median of the second half (upper half) of the data.
**Lower half** (first half): 10, 11
**Upper half** (second half): 12, 14
3. **Find Q1:**
- The median of 10 and 11 is \( \frac{10 + 11}{2} = 10.5 \)
4. **Find Q3:**
- The median of 12 and 14 is \( \frac{12 + 14}{2} = 13 \)
5. **Calculate IQR:**
- \( \text{IQR} = Q3 - Q1 = 13 - 10.5 = 2.5 \)
Therefore, the IQR is **2.5**.
Given the dispensing trials: 12, 11, 10, 11, 14
1. **Sort the data:**
- The sorted data: 10, 11, 11, 12, 14
2. **Determine Q1 and Q3:**
- Q1 is the median of the first half (lower half) of the data.
- Q3 is the median of the second half (upper half) of the data.
**Lower half** (first half): 10, 11
**Upper half** (second half): 12, 14
3. **Find Q1:**
- The median of 10 and 11 is \( \frac{10 + 11}{2} = 10.5 \)
4. **Find Q3:**
- The median of 12 and 14 is \( \frac{12 + 14}{2} = 13 \)
5. **Calculate IQR:**
- \( \text{IQR} = Q3 - Q1 = 13 - 10.5 = 2.5 \)
Therefore, the IQR is **2.5**.