Find the interquartile range of the given dataset. 11, 13, 22, 17, 14, 21, 27, 15
To find the interquartile range (IQR) of a dataset, we first need to find the first quartile (Q1) and the third quartile (Q3).
1. Arrange the dataset in ascending order: 11, 13, 14, 15, 17, 21, 22, 27
2. Find the median of the dataset. Since there are 8 numbers in the dataset, the median is the average of the 4th and 5th numbers: (15 + 17) / 2 = 16
3. Q1 is the median of the lower half of the dataset, so we find the median of the numbers below 16: 11, 13, 14, 15 = (13 + 14) / 2 = 13.5
4. Q3 is the median of the upper half of the dataset, so we find the median of the numbers above 16: 17, 21, 22, 27 = (21 + 22) / 2 = 21.5
5. Finally, calculate the interquartile range by subtracting Q1 from Q3: IQR = Q3 - Q1 = 21.5 - 13.5 = 8
Therefore, the interquartile range of the given dataset is 8.