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 set

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

Step2: Calculate the inter - quartile range (IQR)

Find the first quartile \(Q_1\). The first half of the data is \(6, 10, 12, 12\). The median of this half is \(\frac{10 + 12}{2}=11\).
Find the third quartile \(Q_3\). The second half of the data is \(14, 16, 22\). The median of this half is \(16\).
The inter - quartile range \(IQR = Q_3-Q_1=16 - 11 = 5\).

Step3: Determine the outlier boundaries

The lower boundary is \(Q_1-1.5\times IQR=11-1.5\times5 = 11 - 7.5=3.5\).
The upper boundary is \(Q_3 + 1.5\times IQR=16+1.5\times5=16 + 7.5 = 23.5\).
Any value less than \(3.5\) or greater than \(23.5\) is an outlier. Since \(6>3.5\) and \(22<23.5\), we can also check by visual inspection of the sorted data. The value \(6\) is relatively far from the other values in the sorted set \(6, 10, 12, 12, 13, 13, 14, 16, 22\) compared to the spread of the other data points.

Answer:

A. 6