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Chapter 3: Problem 89

Explain the concept of the percentile rank for an observation of a data set.

Short Answer

Expert verified
The percentile rank of an observation in a data set refers to the percentage of values in the data set that are less than or equal to that observation. It is calculated by dividing the number of values below the observation by the total number of values and multiplying by 100.

Step by step solution

01

Understand Percentiles

Percentiles are measures that divide a set of observations into 100 equal parts. They are used in statistics to give a relative standing of an observation within a data set.
02

Define Percentile Rank

The percentile rank of a given observation is the percentage of observations in a data set that are less than or equal to that observation. It gives us the relative standing of an observation within a data dataset.
03

Explain Calculation of Percentile Rank

To calculate the percentile rank, arrange the data in increasing order, and then the formula for finding the percentile rank is: \[ Percentile\,Rank = \left( \frac{number\,of\,values\,below\,x}{total\,number\,of\,values} \right) \times 100 \] Here, \(x\) is the observation whose percentile rank we want to find.

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