A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information:
Median = 202.2
lower fourth = 196.0
Upper fourth = 216.8 $$\begin{array} { l l l l }
\text { Three smallest observations } & 125.8 & 188.1 & 193.7 \
\text { Three largest observations } & 221.3 & 230.5 & 250.2
\end{array}$$ Are there any outliers in the sample? Any extreme outliers?

Question

A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information:
Median = 202.2
lower fourth = 196.0
Upper fourth = 216.8 $$\begin{array} { l l l l } 
\text { Three smallest observations } & 125.8 & 188.1 & 193.7 \
\text { Three largest observations } & 221.3 & 230.5 & 250.2
\end{array}$$ Are there any outliers in the sample? Any extreme outliers?

Quizplus · Accepted Answer

The Answer is 1.5(IQR) = 1.5(216.8-196.0) = 31.2 and 3(IQR) = 3(216.8-196.0) = 62.4.
Mild outliers: observations below 196-31.2 = 164.6 or above 216.8+31.2=248.
Extreme outliers: observations below 196-62.4 = 133.6 or above 216.8+62.4 = 279.2.
Of the observations given, 125.8 is an extreme outlier and 250.2 is a mild outlier.

A Sample of 20 Glass Bottles of a Particular Type