Question

quartiles - item 34001
find the interquartile range of the data set shown.
the interquartile range is

Explanation:

Step1: Find the first quartile ($Q_1$)

The first half of the data set is $5,8,12,12$. The median of this half is $\frac{8 + 12}{2}=10$.

Step2: Find the third quartile ($Q_3$)

The second half of the data set is $18,20,22,23$. The median of this half is $\frac{20+22}{2} = 21$.

Step3: Calculate the inter - quartile range (IQR)

The formula for IQR is $IQR=Q_3 - Q_1$. Substitute $Q_1 = 10$ and $Q_3=21$ into the formula: $IQR=21 - 10=11$.

Answer:

$11$