Find the interquartile range of the given dataset.
11, 13, 22, 17, 14, 21, 27, 15
(1 point)
Responses
21.5
21.5
8
8
6.5
6.5
13.5
To find the interquartile range, we first need to find the median (Q2) of the dataset.
Arranging the data in ascending order: 11, 13, 14, 15, 17, 21, 22, 27
Q2 is the median, which is the middle value of the dataset, so Q2 = 17.
Next, we need to find the median of the lower half (Q1) and the median of the upper half (Q3).
Q1 = median of the lower half = (13 + 14) / 2 = 13.5
Q3 = median of the upper half = (21 + 22) / 2 = 21.5
Finally, we can calculate the interquartile range:
Interquartile Range = Q3 - Q1 = 21.5 - 13.5 = 8
Therefore, the interquartile range of the given dataset is 8.
To find the interquartile range of the dataset, we need to first calculate 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: Calculate Q1:
The formula to find Q1 is (n+1)/4, where n is the number of data points in the dataset.
(8+1)/4 = 9/4 = 2.25
Since 2.25 is not an integer, we need to take the average of the 2nd and 3rd values.
Q1 = (13 + 14)/2 = 13.5
Step 3: Calculate Q3:
The formula to find Q3 is (3 * (n+1))/4.
3 * (8+1) / 4 = 27/4 = 6.75
Since 6.75 is not an integer, we need to take the average of the 6th and 7th values.
Q3 = (21 + 22)/2 = 21.5
Step 4: Calculate the interquartile range:
Interquartile range = Q3 - Q1 = 21.5 - 13.5 = 8
Therefore, the interquartile range of the given dataset is 8.