Question

Find the inter quartile range for the data: $9,11,15,19,17,13,7.$

• A. $7$
• B. $6$
• C. $8$
• D. None of the above

Answer 1

The correct option is C $8$

Interquartlie is the difference between upper quartile and lower quartile.

Lower quartile is the median of the lower half of the data set.

Upper quartile is the median of the upper half of the data set.

Given data set is $9,11,15,19,17,13,7$

Arranging the data set in ascending order we get $7,9,11,13,15,17,19$

Number of values in the data set is $n=7$

Lower quartile is given by $Q_1=\frac{n+1}{4}=\frac{7+1}{4}=\frac{8}{4}=2^{nd}value$

Therefore, the lower quartile is $Q_1=9$

Upper quartile is given by $Q_3=\frac{3}{4}(n+1)=\frac{3}{4}(7+1)=\frac{3}{4}\left(8\right)=6^{th}value$

Therefore, the upper quartile is $Q_3=17$

Therefore, the inter quartile is given by $Q_3-Q_1=17-9=8$