Question

in the data set below, what is the interquartile range? 41 49 54 56 62 62

Explanation:

Step1: Find the median of the lower half ($Q_1$)

The data set is $41,49,54,56,62,62$. The lower half is $41,49,54$. The median of this lower - half is $\frac{49 + 54}{2}=51.5$.

Step2: Find the median of the upper half ($Q_3$)

The upper half is $56,62,62$. The median of this upper - half is $\frac{62+62}{2}=62$.

Step3: Calculate the inter - quartile range (IQR)

The formula for IQR is $IQR = Q_3−Q_1$. Substitute $Q_1 = 51.5$ and $Q_3 = 62$ into the formula: $IQR=62 - 51.5$.

Answer:

$10.5$