what is the interquartile range for the data set? 89, 91, 95, 112, 118, 83, 85, 104, 118, 125, 134, 138…

Explanation:

Step1: Sort the data set

$83, 85, 89, 91, 95, 104, 112, 118, 118, 125, 134, 138$

Step2: Find the median (Q2)

Since there are 12 data - points, the median is the average of the 6th and 7th ordered values. $Q2=\frac{104 + 112}{2}=108$

Step3: Find the lower half and Q1

The lower half is $83, 85, 89, 91, 95, 104$. The median of the lower half (Q1) is the average of the 3rd and 4th ordered values. $Q1=\frac{89+91}{2}=90$

Step4: Find the upper half and Q3

The upper half is $112, 118, 118, 125, 134, 138$. The median of the upper half (Q3) is the average of the 3rd and 4th ordered values. $Q3=\frac{118 + 125}{2}=121.5$

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=121.5−90 = 31.5$

Answer:

$31.5$