Are there outliers in the smolt data Refer to Exercise

Step 1 of 6

Exercise 1.64 data:

\(\begin{array}{llllllllll}
\hline 57.6 & 54.8 & 63.4 & 57.0 & 54.7 & 42.3 & 63.6 & 55.5 & 33.5 & 63.3 \\
58.3 & 42.1 & 56.1 & 47.8 & 56.1 & 55.9 & 38.8 & 49.7 & 42.3 & 45.6 \\
69.0 & 50.4 & 53.0 & 38.3 & 60.4 & 49.3 & 42.8 & 44.5 & 46.4 & 44.3 \\
58.9 & 42.1 & 47.6 & 47.9 & 69.2 & 46.6 & 68.1 & 42.8 & 45.6 & 47.3 \\
59.6 & 37.8 & 53.9 & 43.2 & 51.4 & 64.5 & 43.8 & 42.7 & 50.9 & 43.8 \\
\hline
\end{array}\)

The interquartile range IQR is the distance between the first and third quartiles:

\(I Q R=Q_{3}-Q_{1}\)

The first quartile \(Q_{1}\) is the median of the observations whose positions in the ordered list are to the left of the location of the overall median. The third quartile \(Q_{3}\) is the median of the observations whose positions in the ordered list are to the right of the location of the overall median.

\(\begin{array}{l}
Q_{3}=56.8 \\
Q_{1}=43.8
\end{array}\)

Therefore, \(I Q R=56.8-43.8=13\)