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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

1 answer

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 \( \boxed{2.5} \).