Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
(1 point)
Responses
8
8
21.5
21.5
6.5
6.5
13.5
13.5
To find the interquartile range, first find the median of the dataset. The dataset arranged in order is:
11, 13, 14, 15, 17, 21, 22, 27
The median of the dataset is the average of the two middle numbers, which are 15 and 17. The median is (15 + 17) / 2 = 16.
Next, find the median of the lower half of the dataset (from the beginning up to the median). The lower half is 11, 13, 14, and 15. The median of the lower half is the average of the two middle numbers, which are 13 and 14. The median of the lower half is (13 + 14) / 2 = 13.5.
Similarly, find the median of the upper half of the dataset (from the median to the end). The upper half is 17, 21, 22, and 27. The median of the upper half is the average of the two middle numbers, which are 21 and 22. The median of the upper half is (21 + 22) / 2 = 21.5.
The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1), which are 21.5 and 13.5 respectively.
Interquartile range = Q3 - Q1 = 21.5 - 13.5 = 8
Therefore, the interquartile range of the given dataset is 8.