Question

Find the interquartile range of
the given dataset.
11,13,22,17,14,21,27,15
choose one
6.5
8
21.5
13.5

Answer 1

To find the interquartile range (IQR) of the given dataset, we first need to sort the data in ascending order:

**Sorted data:** 11, 13, 14, 15, 17, 21, 22, 27

Next, we'll find the first quartile (Q1) and the third quartile (Q3).

- The first quartile (Q1) is the median of the first half of the data. For the dataset above, the first half is: 11, 13, 14, 15. The median of these four numbers is the average of the two middle numbers (13 and 14):

\[
Q1 = \frac{13 + 14}{2} = \frac{27}{2} = 13.5
\]

- The third quartile (Q3) is the median of the second half of the data. The second half of the dataset is: 17, 21, 22, 27. The median of these four numbers is the average of the two middle numbers (21 and 22):

\[
Q3 = \frac{21 + 22}{2} = \frac{43}{2} = 21.5
\]

Now, we can find the interquartile range (IQR) using the formula:

\[
\text{IQR} = Q3 - Q1
\]

Calculating this gives:

\[
\text{IQR} = 21.5 - 13.5 = 8
\]

Thus, the interquartile range of the dataset is **8**. Therefore, the answer is **8**.