Percentiles measure a result in comparison to the other results of the study. For example, if you score in the 50th percentile on a test, that means you did better than half the participants and worse than half the participants. The 85th percentile is often used to determine speed limits for roads. The theory assumes that most drivers are reasonable and do not want to get in an accident, but do want to get to their destination as quickly as possible. Therefore, a speed at which 85 per cent of people drive is figured to be the highest safe speed for that road.

- Skill level:
- Moderately Easy

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## Instructions

- 1
Divide 85 by 100 to convert the percentage to a decimal of 0.85.

- 2
Multiply 0.85 by the number of results in the study and add 0.5. For example, if the study includes 300 car speeds, multiply 300 by 0.85 to get 255 and add 0.5 to get 255.5.

- 3
Order your data from smallest to largest. With cars, arrange the speeds from slowest to fastest.

- 4
Locate the data that corresponds to the integer calculated in Step 2. If the number is a whole number, the corresponding data point is the 85th percentile. If the number is a decimal, find the data points above and below the number. In this example, you would find the 255th and 256th slowest cars.

- 5
Plug in the values for the two numbers and the decimal of the result into the following equation to find the 85th percentile: 85th percentile = (1-d)

*x + d*xx, where d is the decimal from the Step 2 result, x is the data point corresponding to the integer below the Step 2 result and xx is the data point corresponding to the integer above the Step 2 result. In this example, since the result is 255.5, the decimal equals 0.5, the data point below is the 255th slowest car and the data point above is the 256th slowest car. If the 255th slowest car is going 55mph and the 256th slowest car is going 57mph, your equation would be 85th percentile = (1-0.5)*55 + 0.5*57, which simplifies to 56mph as the 85th percentile.