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