Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
(1 point)
Responses
8
8
6.5
6.5
21.5
21.5
13.5
out of these questions Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
(1 point)
Responses
8
8
6.5
6.5
21.5
21.5
13.5
The given dataset is: 11, 13, 22, 17, 14, 21, 27, 15
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3) of the dataset:
Sort the dataset:
11, 13, 14, 15, 17, 21, 22, 27
Q1 is the median of the lower half of the data set, which is between 13 and 14:
Q1 = (13 + 14) / 2 = 13.5
Q3 is the median of the upper half of the data set, which is between 21 and 22:
Q3 = (21 + 22) / 2 = 21.5
Now, calculate the interquartile range:
IQR = Q3 - Q1
IQR = 21.5 - 13.5
IQR = 8
Therefore, the interquartile range of the given dataset is 8.
The interquartile range is calculated by finding the median of the upper half of the data set (Q3) and subtracting the median of the lower half of the data set (Q1).
First, let's find the first quartile (Q1) and the third quartile (Q3) of the dataset:
Sorted dataset: 11, 13, 14, 15, 17, 21, 22, 27
Q1 = 14
Q3 = 21
Now, we calculate the interquartile range:
IQR = Q3 - Q1
IQR = 21 - 14
IQR = 7
Therefore, the interquartile range of the given dataset is 7.