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In the data set below, what is the interquartile range?

3 3 4 7 9

1 answer

To find the interquartile range (IQR) of the dataset, we first need to determine the first quartile (Q1) and the third quartile (Q3).

  1. Arrange the data in ascending order: The data is already arranged: 3, 3, 4, 7, 9.

  2. Calculate Q1 (the first quartile): Q1 is the median of the first half of the data. The first half of the dataset (excluding the median if necessary) is:

    • 3, 3 The median of this subset is: \[ Q1 = \frac{3 + 3}{2} = 3 \]

  3. Calculate Q3 (the third quartile): Q3 is the median of the second half of the data. The second half of the dataset is:

    • 4, 7, 9 The median of this subset is: \[ Q3 = 7 \]

  4. Calculate the interquartile range (IQR): The IQR is the difference between Q3 and Q1: \[ \text{IQR} = Q3 - Q1 = 7 - 3 = 4 \]

Thus, the interquartile range is 4.