Introduction to finding outliers in a data set .

In a survey, 11 people gave the following ratings for a local politician (on a scale of 0 to 100 ).
\[
12,40,41,42,44,48,49,53,55,55,56
\]

Identify all values that are outliers.
If there is more than one outlier, separate them with commas.
If there are no outliers, click on "None".

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.