in the data set below, what is the interquartile range? 22 41 89 87 25 13 83
in the data set below, what is the interquartile range? 22 41 89 87 25 13 83
Answer
Explanation:
Step1: Sort the data set
$13, 22, 25, 41, 83, 87, 89$
Step2: Find the median (Q2)
Since there are 7 data - points, the median is the 4th value. So, $Q2 = 41$.
Step3: Find the lower half and Q1
The lower half is $13, 22, 25$. The median of the lower half (Q1) is 22.
Step4: Find the upper half and Q3
The upper half is $83, 87, 89$. The median of the upper half (Q3) is 87.
Step5: Calculate the inter - quartile range (IQR)
$IQR=Q3 - Q1=87 - 22 = 65$
Answer:
65