Respuesta :
Given set :
154,109,137,115,152,140,154,178,80,103,126,126,137,165,165,129,200,148.
Rewrite the given data set from least to highest values.
80, 103, 109, 115, 126, 126, 129, 137, 137, 140, 148, 152, 154, 154, 165, 165, 178, 200.
Recall that a data point is an outlier if it is over 1.5 times the IQR below the first quartile or 1.5 times the IQR above the third quartile.
We know that
[tex]\text{IQR}=Q_3-Q_1[/tex][tex]Q_3=The\text{ third quartile = The median of the upper half of the data set.}[/tex][tex]Q_1=The\text{ first quartile = The median of the lower half of the data set.}[/tex]The upper half of the data set is
{137, 140, 148, 152, 154, 154, 165, 165, 178, 200}
The number of data in the set is even.
There are two middle terms in this upper half of the given set. That are 154 and 154.
[tex]Q_3=\frac{154+154}{2}=154[/tex]The lower half of the data set is
{80, 103, 109, 115, 126, 126, 129, 137, 137, 140}
The number of data in the set is even.
There are two middle terms in this lower half of the given set. Which are 126 and 126.
[tex]Q_1=\frac{126+126}{2}=126[/tex]Substitute known values in the IQR formula.
[tex]\text{IQR}=154-126=28[/tex]We get IQR=28.
[tex]\text{HIgher outlier }\ge Q_3+(1.5\times IQR)[/tex][tex]undefined[/tex]