Percentiles are values that divide a data set into 100 equal parts, indicating the relative standing of an observation within the data. They are commonly used to understand and interpret the distribution of data points.
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The 50th percentile is known as the median, which divides the data set into two equal halves.
To find a specific percentile, you first need to arrange the data in ascending order.
The formula for finding the rank of a percentile is $P_k = \frac{k}{100} \cdot (N+1)$, where $k$ is the desired percentile and $N$ is the number of observations.
Percentiles can be used to identify outliers by examining values at extreme percentiles such as the 1st or 99th percentiles.
In a normal distribution, approximately 68% of data falls between the 16th and 84th percentiles.
Review Questions
What is the significance of the 50th percentile in a data set?
How do you determine which value corresponds to a specific percentile in an ordered data set?
Why are percentiles useful in identifying outliers?
Related terms
Quartiles: Values that divide a data set into four equal parts. The first quartile (Q1) represents the 25th percentile, and so on.