Math  /  Data & Statistics

Question44. In 2007 there were 768 "oldies" radio stations in the United States. If one station finds that 84 stations have a larger daily audience than it has, what percentile does this station come closest to in the daily audience rankings? (Source: Radio-locator.com)

Studdy Solution

STEP 1

1. There are a total of 768 "oldies" radio stations.
2. The station in question has 84 stations with a larger daily audience.

STEP 2

1. Determine the rank of the station in question.
2. Calculate the percentile rank of the station.

STEP 3

Determine the rank of the station by subtracting the number of stations with a larger audience from the total number of stations.
Rank=76884 \text{Rank} = 768 - 84
Rank=684 \text{Rank} = 684

STEP 4

Calculate the percentile rank using the formula:
Percentile=(RankTotal number of stations)×100 \text{Percentile} = \left( \frac{\text{Rank}}{\text{Total number of stations}} \right) \times 100
Percentile=(684768)×100 \text{Percentile} = \left( \frac{684}{768} \right) \times 100
Percentile=0.890625×100 \text{Percentile} = 0.890625 \times 100
Percentile=89.0625 \text{Percentile} = 89.0625
Round to the nearest whole number:
Percentile89 \text{Percentile} \approx 89
The station is closest to the 89th percentile in the daily audience rankings.

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