Number of outliers #=2#

To calculate the interquartile range, first sort the values in ascending order:
\[58,\,\,\,60,\,\,\,70,\,\,\,82,\,\,\,82,\,\,\,83,\,\,\,86,\,\,\,86,\,\,\,90,\,\,\,94,\,\,\,99,\,\,\,99,\,\,\,104\]

Next, calculate the first quartile. To find the index #i_1# of the first quartile (#Q=1#), use the following formula:
\[\begin{array}{rcl}
i_1 &=& \cfrac{Q}{4}(n-1)+1\\
&=& \cfrac{1}{4}(13 - 1) + 1=4
\end{array}\]
Since #i_1=4# is an integer, the first quartile is the score located at the #4^{th}# position of the ordered data:
\[X_{4} = 82\]
Next, calculate the third quartile. To find the index #i_3# of the third quartile (#Q=3#), use the following formula:
\[\begin{array}{rcl}
i_3 &=& \cfrac{Q}{4}(n-1)+1\\
&=& \cfrac{3}{4}(13 - 1) + 1=10
\end{array}\]
Since #i_3=10# is an integer, the third quartile is the score located at the #10^{th}# position of the ordered data:
\[X_{10} = 94\]
Calculate the interquartile range:
\[\text{IQR}=Q_3-Q_1=94-82=12\]
According to the Interquartile Range Rule, a score #X# is considered an outlier if:

• The score lies more than #1.5\cdot IQR\,# below the first quartile: #X < (Q_1 - 1.5\cdot IQR)#
  \[Q_1 - 1.5\cdot IQR = 82 - 1.5 \cdot 12 = 64.0\]
• The score lies more than #1.5\cdot IQR\,# above the third quartile: #X > (Q_3 + 1.5\cdot IQR)#
  \[Q_3 + 1.5\cdot IQR = 94 + 1.5 \cdot 12 = 112.0\]

This means that any score #X<64.0# or #X>112.0# should be considered an outlier, of which there are #2# in the sample, namely: #60# and #58#.