Step 1 :Arrange the data in ascending order: \(12, 40, 41, 42, 44, 48, 49, 53, 55, 55, 56\)
Step 2 :Find the lower quartile (Q1), which is the median of the first half of the data. The first half is the first 5 numbers: \(12, 40, 41, 42, 44\). The median of these 5 numbers is \(41\)
Step 3 :Find the upper quartile (Q3), which is the median of the second half of the data. The second half is the last 5 numbers: \(53, 55, 55, 55, 56\). The median of these 5 numbers is \(55\)
Step 4 :Calculate the interquartile range (IQR), which is Q3 - Q1: \(IQR = 55 - 41 = 14\)
Step 5 :Calculate the lower bound for outliers, which is Q1 - 1.5*IQR: \(Lower bound = 41 - 1.5*14 = 41 - 21 = 20\)
Step 6 :Calculate the upper bound for outliers, which is Q3 + 1.5*IQR: \(Upper bound = 55 + 1.5*14 = 55 + 21 = 76\)
Step 7 :Identify any numbers in the data set that are less than the lower bound or greater than the upper bound. These are the outliers.
Step 8 :\(\boxed{12}\) is less than the lower bound of \(20\), so \(12\) is an outlier.