To find the range and the interquartile range (IQR) of the dataset, we can follow these steps:
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Calculate the range: The range is calculated as the difference between the maximum and minimum values in the dataset.
- Maximum height = 82 inches
- Minimum height = 68 inches
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 82 - 68 = 14 \]
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Calculate the interquartile range (IQR): The IQR is the difference between the first quartile (Q1) and the third quartile (Q3).
First, let's arrange the data in ascending order:
- 68, 70, 74, 75, 78, 82
Next, we find Q1 (the median of the first half) and Q3 (the median of the second half).
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For Q1 (the first half): 68, 70, 74 \[ Q1 = 70 \] (the median of the first three numbers)
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For Q3 (the second half): 75, 78, 82 \[ Q3 = 78 \] (the median of the last three numbers)
Now, we can calculate the IQR: \[ \text{IQR} = Q3 - Q1 = 78 - 70 = 8 \]
Therefore, the final results are:
- Range = 14
- Interquartile Range = 8
The correct response is: The range is 14, and the interquartile range is 8.