To determine which of the given options equals 1.5 times the Interquartile Range (IQR) for the data set, we need to follow these steps:
1. Identify [tex]$Q_1$[/tex] and [tex]$Q_3$[/tex]:
The first quartile ([tex]$Q_1$[/tex]) is 12, and the third quartile ([tex]$Q_3$[/tex]) is 16.
2. Calculate the Interquartile Range (IQR):
The IQR is defined as the difference between [tex]$Q_3$[/tex] and [tex]$Q_1$[/tex]:
[tex]\[
IQR = Q_3 - Q_1
\][/tex]
Substituting the given values:
[tex]\[
IQR = 16 - 12
\][/tex]
[tex]\[
IQR = 4
\][/tex]
3. Calculate 1.5 times the IQR:
We multiply the IQR by 1.5:
[tex]\[
1.5 \times IQR = 1.5 \times 4
\][/tex]
[tex]\[
1.5 \times IQR = 6
\][/tex]
Therefore, 1.5 times the IQR equals 6.
Among the given options, the correct answer is 6.
