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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 =40−10 =30 Hence, the inter-quartile range of the given data is 30.

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