Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
To find the interquartile range (IQR), we first need to find the median (Q2) of the dataset.
11, 13, 14, 15, 17, 21, 22, 27
Q2 = (15 + 17)/2 = 16
Next, we need to find the median of the lower half of the dataset (Q1) and the median of the upper half of the dataset (Q3).
Lower half: 11, 13, 14, 15
Q1 = (13 + 14)/2 = 13.5
Upper half: 17, 21, 22, 27
Q3 = (21 + 22)/2 = 21.5
Finally, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 21.5 - 13.5 = 8
Therefore, the interquartile range of the given dataset is 8.
To find the interquartile range (IQR) of a dataset, you first need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the dataset in ascending order:
11, 13, 14, 15, 17, 21, 22, 27
Step 2: Find the median of the dataset, also known as the second quartile (Q2).
Since we have 8 numbers in the dataset, the median is the average of the two middle numbers: (15 + 17) / 2 = 16
Step 3: Find Q1, which is the median of the lower half of the dataset.
Considering the left half of the dataset: 11, 13, 14, 15
Since we have 4 numbers, the median of the lower half is the middle number: 14
Step 4: Find Q3, which is the median of the upper half of the dataset.
Considering the right half of the dataset: 17, 21, 22, 27
Since we have 4 numbers, the median of the upper half is the middle number: 21
Step 5: Calculate the interquartile range (IQR) by subtracting Q1 from Q3.
IQR = Q3 - Q1 = 21 - 14 = 7
Therefore, the interquartile range of the given dataset is 7.