Find the interquartile range of the given dataset. 11, 13, 22, 17, 14, 21, 27, 15 (1 point) Responses 6.5 6.5 8 8 13.5 13.5 21.5
To find the interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3).
1. Arrange the dataset in ascending order: 11, 13, 14, 15, 17, 21, 22, 27
2. Calculate the median of the entire dataset:
Median = (15 + 17) / 2 = 16
3. Q1 is the median of the lower half of the dataset (11, 13, 14, 15):
Q1 = (13 + 14) / 2 = 13.5
4. Q3 is the median of the upper half of the dataset (17, 21, 22, 27):
Q3 = (21 + 22) / 2 = 21.5
Finally, the interquartile range (IQR) is calculated as follows:
IQR = Q3 - Q1
IQR = 21.5 - 13.5
IQR = 8
Therefore, the interquartile range of the given dataset is 8.