Question

in the data set below, what is the interquartile range? 27 23 15 57 27 69 65 13 84 37 49 96

Explanation:

Step1: Sort the data

Sort the data set in ascending order: $13,15,23,27,27,37,49,57,65,69,84,96$

Step2: Find the median (Q2)

Since there are $n = 12$ data points, the median is the average of the $6^{th}$ and $7^{th}$ values. $Q2=\frac{37 + 49}{2}=43$

Step3: Find Q1

The lower - half of the data is $13,15,23,27,27,37$. Since there are $n = 6$ data points in the lower - half, $Q1=\frac{23+27}{2}=25$

Step4: Find Q3

The upper - half of the data is $49,57,65,69,84,96$. Since there are $n = 6$ data points in the upper - half, $Q3=\frac{65 + 69}{2}=67$

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1$
$IQR=67-25$

Answer:

$42$