# Computing Quantiles-Percentiles, Quintiles, Deciles, Quarters

## Overview:

• Similar to Mean, Median and Mode a Quantile is also a statistical measure of location.
• Quantile indicates a point in distribution below which, a portion of the data lies.
• Quantile is also called as Fractile as it locates the place in distribution below which, a specific fraction of the distribution lies.
• Quantile is a generic term.  The measures percentile, quintile, decile and quartiles are all quantiles that divide a distribution into portions.
• Percentiles: They divide the distribution into hundredths.
• Quintiles: They divide the distribution as parts of fifths.
• Deciles: They divide the distribution into parts of tenths.
• Quarters: They divide the distribution into quarters.

## Finding quantiles for a Pandas.series:

• Series.quartile() function returns the specific value of a quantile based on the parameter ‘q‘.
• Here is a table that summarizes various quantiles:
 Value of ‘q‘ Quantile 0.05 1st quintile 0.1 1st Decile/2nd quintile 0.2 2nd Decile/4th quintile 0.25 1st quarter/5th quintile/ 25th percentile 0.3 3rd Decile/6th quintile/ 30th percentile 0.4 4th Decile/8th quintile/ 40th percentile 0.5 1st half/2nd quarter/5th Decile/10th quintile/50th percentile 0.6 6th Decile/12th quintile/60th percentile 0.7 7th Decile/14th quintile/70th percentile 0.75 3rd quarter/15th quintile/ 75th percentile 0.9 9th Decile/18th quintile/90th percentile 1.0 10th Decile/20th quintile/100th percentile

## Example:

The example below loads a JSON string of student scores into a pandas.series and calculates the 1st Quarter, 2nd Quarter and 3rd Quarter scores. Also it finds the 1st and 100th percentiles scores.

 # Example Python program that calculates quantiles import pandas as pds   # Read a JSON file scoreFile = "./scores.json"; dataFrame = pds.read_json(scoreFile);   # Load the score column into a pandas.Series scores = dataFrame["Score"]; print("Scores as loaded into the pandas.Series instance:"); print(scores);   print("First Quartile:%.2f"%scores.quantile(.25)); print("Second Quartile:%.2f"%scores.quantile(.5)); print("Third Quartile:%.2f"%scores.quantile(.75)); print("100th Percentile:%.2f"%scores.quantile(1)); print("1st Percentile:%.2f"%scores.quantile(.1));

## Output:

 Scores as loaded into the pandas.Series instance: 0    65 1    61 2    77 3    82 4    67 5    55 6    53 7    85 8    67 9    96 Name: Score, dtype: int64 First Quartile:62.00 Second Quartile:67.00 Third Quartile:80.75 100th Percentile:96.00 1st Percentile:54.80