ANSWER
The inter-quartile range is 12
EXPLANATION
The given data set is
[tex]12, x,x+6,30[/tex]
If the median is 17, then
[tex] \frac{x + x + 6}{2} = 17[/tex]
[tex]2x + 6 = 2 \times 17[/tex]
[tex]2x + 6= 34[/tex]
[tex]2x = 34 - 6[/tex]
[tex]2x = 28[/tex]
[tex]x = 14[/tex]
Hence , the data set becomes,
[tex]12, 14,20,30[/tex]
The lower quartile is
[tex]Q_1 = \frac{12 +14 }{2} = 13[/tex]
The upper quartile is
[tex]Q_3 = \frac{20 + 30}{2} = 25[/tex]
The inter-quartile range is
[tex]Q_3 - Q_1 = 25 - 13 = 12[/tex]
