Question

Find the inter-quartile range of the following data:
$5,50,30,15,20$

Answer 1

Given, the sample of the data is:
$5,50,30,15,20$

Step 1: Order the data from smallest to largest.
$5,15,20,30,50$

Step 2: Find the median.
Here, we have 5 numbers (odd), so the middle number is the median of the given numbers.
$5,15,\text{20},30,50$

Median $=20$

Step 3: Find the quartiles.

The lower quartile is the median of the data points to the left of the median.
$\text{5,15}$
Here, we have 2 numbers (even), so we will take the average of them.
$\text{Lower quartile}\left(Q_1\right)=\text{average of 5 and 15)}$
$=\frac{5+15}{2}$
$=\frac{20}{2}$
$=10$

The upper quartile is the median of the data points to the right of the median.
$\text{30, 50}$
$\text{Upper quartile}\left(Q_3\right)=\frac{30+50}{2}=\frac{80}{2}=40$

Step 4: Find the inter-quartile range.
Inter-quartile range $=$ Upper quartile $-$ Lower quartile
$=40-10$
$=30$

Hence, the inter-quartile range of the given data is $30.$