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

1 2 2 2 4 4 4 4 7 7 9

1 answer

To calculate the interquartile range (IQR), you need to follow these steps:

  1. Order the data: The data is already ordered: \(1, 2, 2, 2, 4, 4, 4, 4, 7, 7, 9\)

  2. Determine the quartiles:

    • Find the median (Q2): The median divides the data into two halves. Since there are 11 data points, the median is the 6th value. \[ Q2 = 4 \]

    • Find Q1: This is the median of the lower half (the first 5 values): \(1, 2, 2, 2, 4\) The median of this set is the 3rd value: \[ Q1 = 2 \]

    • Find Q3: This is the median of the upper half (the last 5 values): \(4, 4, 7, 7, 9\) The median of this set is the 3rd value: \[ Q3 = 7 \]

  3. Calculate the interquartile range (IQR): \[ IQR = Q3 - Q1 = 7 - 2 = 5 \]

Thus, the interquartile range is 5.