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

Question

1 1 3 7 9

Answer 1

To find the interquartile range (IQR) of the given data set (1, 1, 3, 7, 9), follow these steps:

1. Organize the data (though in this case, it is already sorted):

   • 1, 1, 3, 7, 9

2. Determine the quartiles:

   • Q1 (First Quartile): This is the median of the first half of the data. The first half is (1, 1, 3). The median of this subset is 1.
   • Q3 (Third Quartile): This is the median of the second half of the data. The second half is (3, 7, 9). The median of this subset is 7.

3. Calculate the interquartile range (IQR): \[ IQR = Q3 - Q1 = 7 - 1 = 6 \]

So, the interquartile range of the data set is 6.