Determine the interquartile range and identify the outlier for the following data set:
18, 17, 3, 22, 9, 7, 10, 48, 10, 10, 10, 13
IQR:
Outlier:
To determine the interquartile range (IQR), we first need to find the first and third quartiles.
1. First, we need to arrange the data set in ascending order:
3, 7, 9, 10, 10, 10, 10, 13, 17, 18, 22, 48
2. Next, we find the median of the lower half of the data set (Q1):
Q1 = median of (7, 9, 10, 10) = (9 + 10) / 2 = 9.5
3. Then, we find the median of the upper half of the data set (Q3):
Q3 = median of (13, 17, 18, 22) = (17 + 18) / 2 = 17.5
4. Now, we can calculate the IQR:
IQR = Q3 - Q1 = 17.5 - 9.5 = 8
Therefore, the interquartile range (IQR) for the data set is 8.
To identify the outlier, we need to use the IQR rule which states that any value below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered an outlier.
1.5 * 8 = 12
Q1 - 12 = 9.5 - 12 = -2.5
Q3 + 12 = 17.5 + 12 = 29.5
Therefore, any values below -2.5 or above 29.5 would be considered outliers. Looking at the data set, the value 48 is the outlier as it is greater than 29.5.