identify the outlier for the following set:
2.4,5.3,3.5,22.6,1.8,2.1,4.6
The outlier in this set is 22.6.
To identify the outlier in the given set (2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6), we can use a simple rule known as the "1.5 x IQR" rule.
1. First, let's sort the set in ascending order:
1.8, 2.1, 2.4, 3.5, 4.6, 5.3, 22.6
2. Next, we need to calculate the Interquartile Range (IQR). To do this, we find the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data set (1.8, 2.1, 2.4), which gives us Q1 = 2.1.
Q3 is the median of the upper half of the data set (4.6, 5.3, 22.6), which gives us Q3 = 5.3.
Therefore, the IQR = Q3 - Q1 = 5.3 - 2.1 = 3.2.
3. Finally, we apply the "1.5 x IQR" rule to identify any outliers. According to this rule, any data point that is more than 1.5 times the IQR away from either Q1 or Q3 can be considered an outlier.
Lower threshold = Q1 - (1.5 x IQR) = 2.1 - (1.5 x 3.2) = 2.1 - 4.8 = -2.7
Upper threshold = Q3 + (1.5 x IQR) = 5.3 + (1.5 x 3.2) = 5.3 + 4.8 = 10.1
Based on these thresholds, any values below -2.7 or above 10.1 can be considered outliers.
Therefore, the outlier in the given set is 22.6.