What Quantile is
Quantiles are points that divide a sample or population into equal parts. They are used to measure the distribution of a dataset. For example, the median is the middle quantile, which splits the data into two equal halves.
Quantiles are calculated using the following steps:
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Sort the data in ascending or descending order.
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Divide the data into the desired number of parts, usually 4 or 5.
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Calculate the position of the quantile point by finding the average of the two adjacent values.
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Calculate the value of the quantile point by looking up the corresponding value in the sorted list.
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Repeat steps 3 and 4 for each quantile point.
Examples
- Quantiles are often used in describing population distributions, such as when examining income distribution or educational attainment.
- Quantiles are used in assessing the performance of a portfolio of investments, where one can look at the quantiles of the returns of the portfolio over time.
- Quantiles are used in constructing confidence intervals, such as when estimating the population mean.
- Quantiles are used in determining cut-off points for evaluating risk, such as when constructing a risk score.
- Quantiles are used to compare the performance of different groups of individuals based on their scores on a particular test.