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

1 1 3 5 9

1 answer

To calculate the interquartile range (IQR) of the dataset \(1, 1, 3, 5, 9\), we first need to find the first quartile (Q1) and the third quartile (Q3):

  1. Order the data (already in order): \(1, 1, 3, 5, 9\)

  2. Find Q1 (the median of the first half):

    • The first half of the data is \(1, 1\).
    • Q1 = median of \(1, 1\) = \(1\)
  3. Find Q3 (the median of the second half):

    • The second half of the data is \(3, 5, 9\).
    • Q3 = median of \(3, 5, 9\) = \(5\)
  4. Calculate the interquartile range (IQR): \[ \text{IQR} = Q3 - Q1 = 5 - 1 = 4 \]

Thus, the interquartile range is \(4\).