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	1^st quintile
0.1	1^st Decile/2^nd quintile
0.2	2^nd Decile/4^th quintile
0.25	1^st quarter/5^th quintile/ 25^th percentile
0.3	3^rd Decile/6^th quintile/ 30^th percentile
0.4	4^th Decile/8^th quintile/ 40^th percentile
0.5	1^st half/2^nd quarter/5^th Decile/10^th quintile/50^th percentile
0.6	6^th Decile/12^th quintile/60^th percentile
0.7	7^th Decile/14^th quintile/70^th percentile
0.75	3^rd quarter/15^th quintile/ 75^th percentile
0.9	9^th Decile/18^th quintile/90^th percentile
1.0	10^th Decile/20^th quintile/100^th percentile

Example:

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