## Related questions with answers

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

VerifiedThe 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)

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

a.

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

b.

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

c.

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

d.

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

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