Problem

Hazardous waste: Following is a list of the number of hazardous waste sites in a sample of states of the United States in a recent year. The list has been sorted into numerical order.
Unknown environment 'tabular'

Source: U.S. Environmental Protection Agency
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Part 1 of 2
(a) What is the 17th  percentile?

The 17an  percentile is .

Part 2 of 2
(b) What is the 62nd  percentile?

The 62nd  percentile is .

Answer

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Answer

The 62nd percentile is 31

Steps

Step 1 :Count the number of data points in the list, which is N=30

Step 2 :Use the formula Position=P100×(N+1) to find the position for the 17th percentile, where P=17

Step 3 :Calculate the position for the 17th percentile, which is Position=17100×(30+1)=5.27

Step 4 :Since the position is not an integer, interpolate between the 5th and 6th data points to find the 17th percentile value

Step 5 :Calculate the 17th percentile value by taking the average of the 5th and 6th data points, which is 11+122=11.5

Step 6 :The 17th percentile is 11.5

Step 7 :Use the same formula to calculate the position for the 62nd percentile, where P=62

Step 8 :Calculate the position for the 62nd percentile, which is Position=62100×(30+1)=19.22

Step 9 :Since the position is not an integer, interpolate between the 19th and 20th data points to find the 62nd percentile value

Step 10 :Calculate the 62nd percentile value by taking the average of the 19th and 20th data points, which is 30+322=31

Step 11 :The 62nd percentile is 31

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