To find the interquartile range (IQR) of the given dataset, follow these steps:
1. **Arrange the data in ascending order:**
\[11, 13, 14, 15, 17, 21, 22, 27\]
2. **Determine the median (Q2):**
The median is the middle value of the dataset. Since there are 8 numbers (an even amount), the median will be the average of the 4th and 5th numbers.
\[
\text{Median (Q2)} = \frac{15 + 17}{2} = 16
\]
3. **Find the first quartile (Q1):**
Q1 is the median of the lower half of the data (excluding the median if the number of data points is odd). The lower half of the data is:
\[11, 13, 14, 15\]
The median of this half is the average of the 2nd and 3rd numbers:
\[
Q1 = \frac{13 + 14}{2} = 13.5
\]
4. **Find the third quartile (Q3):**
Q3 is the median of the upper half of the data (excluding the median if the number of data points is odd). The upper half of the data is:
\[17, 21, 22, 27\]
The median of this half is the average of the 2nd and 3rd numbers:
\[
Q3 = \frac{21 + 22}{2} = 21.5
\]
5. **Calculate the interquartile range (IQR):**
\[
IQR = Q3 - Q1 = 21.5 - 13.5 = 8
\]
Therefore, the interquartile range (IQR) of the dataset is \(8\).
Find the interquartile range of the given dataset. 11, 13, 22, 17, 14, 21, 27, 15 (1 point) Responses 8 8 21.5 21.5 6.5 6.5 13.5
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