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.
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:
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