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Question

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

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Solution

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.
5,15,20,30,50

Median =20

Step 3: Find the quartiles.

The lower quartile is the median of the data points to the left of the median.
5,15
Here, we have 2 numbers (even), so we will take the average of them.
Lower quartile (Q1)=average of 5 and 15)
=5+152
=202
=10

The upper quartile is the median of the data points to the right of the median.
30, 50
Upper quartile (Q3)=30+502=802=40

Step 4: Find the inter-quartile range.
Inter-quartile range = Upper quartile Lower quartile
=4010
=30

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

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