in the data set below, what is the interquartile range? 1 1 1 1 2 6 6 8 8

Answer:

$5$

Explanation:

Step1: Find the median

The data set has $9$ values. The median is the $5^{th}$ value. So, the median is $2$.

Step2: Split the data set

The lower half is $1,1,1,1$. The upper half is $6,6,8,8$.

Step3: Find $Q_1$ and $Q_3$

For the lower half (even number of values), $Q_1=\frac{1 + 1}{2}=1$. For the upper half (even number of values), $Q_3=\frac{6+8}{2}=7$.

Step4: Calculate the inter - quartile range (IQR)

$IQR = Q_3-Q_1$. So, $IQR=7 - 1=5$.