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Question

Room and board costs for selected schools are summarized in this distribution.

Costs (in dollars) Frequency
3000.5-4000.5 5
4000.5-5000.5 6
5000.5-6000.5 18
6000.5-7000.5 24
7000.5-8000.5 19
8000.5-9000.5 8
9000.5-10,000.5 5

Find the approximate percentile rank of each of the following costs. a. 550024th b. 720067th c. 650048th d. 830088th

Solution

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The percentile is the number of values below the value increased by 0.5, divided by the total number of values and multiplied by 100. (ROUND DOWN)

P=(Number of values below X)+0.5n×100P=\dfrac{(\text{Number of values below }X)+0.5}{n}\times 100

a.

P=(Number of values below X)+0.5n×100=(5+6+(499.5/1000)18)+0.585×10024P=\dfrac{(\text{Number of values below }X)+0.5}{n}\times 100=\dfrac{(5+6+(499.5/1000)18)+0.5}{85}\times 100\approx 24

b.

P=(Number of values below X)+0.5n×100=(5+6+18+24+(199.5/1000)19)+0.585×10067P=\dfrac{(\text{Number of values below }X)+0.5}{n}\times 100=\dfrac{(5+6+18+24+(199.5/1000)19)+0.5}{85}\times 100\approx 67

c.

P=(Number of values below X)+0.5n×100=(5+6+18+(499.5/1000)24)+0.585×10048P=\dfrac{(\text{Number of values below }X)+0.5}{n}\times 100=\dfrac{(5+6+18+(499.5/1000)24)+0.5}{85}\times 100\approx 48

d.

P=(Number of values below X)+0.5n×100=(5+6+18+24+19+(299.5/1000)8)+0.585×10088P=\dfrac{(\text{Number of values below }X)+0.5}{n}\times 100=\dfrac{(5+6+18+24+19+(299.5/1000)8)+0.5}{85}\times 100\approx 88

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