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?



The IQR is

Answer 1

To find the Interquartile Range (IQR), we first need to organize the data and find the first (Q1) and third quartiles (Q3).

Given the dispensing trials: \( 12, 11, 10, 11, 14 \)

1. **Sort the data:**
\[
10, 11, 11, 12, 14
\]

2. **Find the first quartile (Q1):**
- Q1 is the median of the first half of the data. In this case, the first half is \( 10, 11 \).
- Since there are 2 numbers, Q1 will be the average of these two values:
\[
Q1 = \frac{10 + 11}{2} = 10.5
\]

3. **Find the third quartile (Q3):**
- Q3 is the median of the second half of the data. The second half is \( 12, 14 \).
- Again, since there are 2 numbers, Q3 will be the average of these two values:
\[
Q3 = \frac{12 + 14}{2} = 13
\]

4. **Calculate the IQR:**
\[
\text{IQR} = Q3 - Q1 = 13 - 10.5 = 2.5
\]

Thus, the Interquartile Range (IQR) of the dispensing trials is \( \boxed{2.5} \).