To calculate the interquartile range (IQR) of the dispensing trials, we first need to arrange the data in ascending order and then find the first quartile (Q1) and the third quartile (Q3).
The data in ascending order is: 10, 11, 11, 12, 14
Step 1: Find Q1 and Q3
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Q1 (the first quartile) is the median of the first half of the data. The first half of the data is 10, 11. Since there are two numbers, Q1 is the average of these two: \[ Q1 = \frac{10 + 11}{2} = 10.5 \]
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Q3 (the third quartile) is the median of the second half of the data. The second half of the data is 11, 12, 14. Since there are three numbers, Q3 is the middle number: \[ Q3 = 12 \]
Step 2: Calculate the IQR The IQR is calculated as follows: \[ \text{IQR} = Q3 - Q1 \] Substituting in the values we found: \[ \text{IQR} = 12 - 10.5 = 1.5 \]
Thus, the IQR of the dispensing trials is 1.5.
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