Question

in the data set below, what is the interquartile range? 25 31 36 36 42 46 50 51 68 70 87 99

Explanation:

Step1: Find the median

The data set has 12 numbers. The median is the average of the 6th and 7th - ordered values. So, median $M=\frac{46 + 50}{2}=48$.

Step2: Split the data into two halves

The lower - half data set is $25,31,36,36,42,46$ and the upper - half data set is $50,51,68,70,87,99$.

Step3: Find the first quartile ($Q_1$)

The first quartile is the median of the lower - half data set. Since there are 6 numbers in the lower - half, $Q_1=\frac{36+36}{2}=36$.

Step4: Find the third quartile ($Q_3$)

The third quartile is the median of the upper - half data set. Since there are 6 numbers in the upper - half, $Q_3=\frac{68 + 70}{2}=69$.

Step5: Calculate the inter - quartile range (IQR)

The inter - quartile range is $IQR = Q_3−Q_1$. So, $IQR=69 - 36=33$.

Answer:

33