Question

the data set represents the number of snails that each person counted on a walk after a rainstorm. 12, 13, 22, 16, 6, 10, 13, 14, 12 what is the outlier of the data? 6 11 15 22

Explanation:

Step1: Sort the data

Sort the data set \(6, 10, 12, 12, 13, 13, 14, 16, 22\).

Step2: Calculate the inter - quartile range (IQR)

Find the median \(Q_2\) of the data. Since \(n = 9\), \(Q_2=\) the 5th value \(=13\).
The lower half of the data is \(6, 10, 12, 12\), and its median \(Q_1=\frac{10 + 12}{2}=11\).
The upper half of the data is \(14, 16, 22\), and its median \(Q_3=\frac{16+22}{2} = 19\).
\(IQR=Q_3 - Q_1=19 - 11 = 8\).

Step3: Determine the outlier boundaries

Lower boundary \(=Q_1-1.5\times IQR=11-1.5\times8=11 - 12=-1\).
Upper boundary \(=Q_3 + 1.5\times IQR=19+1.5\times8=19 + 12=31\).
A value is an outlier if it is less than the lower boundary or greater than the upper boundary.

Answer:

\(22\) is within the calculated boundaries (\(-1<22<31\)), \(6\) is within the boundaries (\(-1 < 6<31\)), \(11\) and \(15\) are not in the original data set. But if we consider the general concept of an outlier as a value that is far from the other values in a simple sense (without strict IQR - based calculation for a very small data set), \(22\) is much larger than most of the other values (\(6,10,12,12,13,13,14,16\)). So the outlier is \(22\).