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?

Answer 1

To find the interquartile range (IQR) of the dispensing trials, we first need to arrange the data in ascending order:

1. The data in order: 10, 11, 11, 12, 14.

Next, we find the first quartile (Q1) and the third quartile (Q3).

1. **Determine Q1** (the median of the first half of the data):
- The first half of the data consists of: 10, 11 (the two values before the median 12)
- Q1 is the average of these two values:
\[
Q1 = \frac{10 + 11}{2} = \frac{21}{2} = 10.5
\]

2. **Determine Q3** (the median of the second half of the data):
- The second half of the data consists of: 12, 14 (the two values after the median 12)
- Q3 is the average of these two values:
\[
Q3 = \frac{12 + 14}{2} = \frac{26}{2} = 13
\]

3. **Calculate the IQR**:
- The interquartile range is calculated as:
\[
IQR = Q3 - Q1 = 13 - 10.5 = 2.5
\]

Therefore, the IQR of the dispensing trials is \( \boxed{2.5} \).