Question

how many outliers are in the following data set? 167, 180, 188, 177, 181, 185, 189 select one: zero one two three four five

Explanation:

Step1: Sort the data set

First, sort the data set \(167, 180, 188, 177, 181, 185, 189\) in ascending order: \(167, 177, 180, 181, 185, 188, 189\).

Step2: Calculate the quartiles

The median (\(Q_2\)) of the data set (with \(n = 7\) data points, the median is the \(\frac{n + 1}{2}\) -th value) is the 4 -th value. So \(Q_2=181\).
The lower half of the data is \(167, 177, 180\). The median of the lower half (\(Q_1\)) is the 2 -nd value, so \(Q_1 = 177\).
The upper half of the data is \(185, 188, 189\). The median of the upper half (\(Q_3\)) is the 2 -nd value of the upper half, so \(Q_3=188\).

Step3: Calculate the inter - quartile range (IQR)

The inter - quartile range \(IQR=Q_3 - Q_1\). So \(IQR = 188-177=11\).

Step4: Determine the outlier boundaries

The lower boundary for outliers is \(Q_1-1.5\times IQR=177 - 1.5\times11=177-16.5 = 160.5\).
The upper boundary for outliers is \(Q_3 + 1.5\times IQR=188+1.5\times11=188 + 16.5=204.5\).

Answer:

A. Zero