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[ Pandas Common Functions](#) * * * `Series.quantile()` is a function in Pandas used to calculate quantiles of a Series. A quantile is a value that divides an ordered dataset into equal parts. Common quantiles include quartiles (25%, 50%, 75%), and the median (50%). Quantiles are important indicators for describing data distribution and help understand the shape of the data and identify outliers. They are widely used in statistical analysis, ranking, income analysis, and other scenarios. * * * ## Basic Syntax and Parameters `quantile()` is a member function of the Series object, called directly using the dot operator. ### Syntax Format Series.quantile(q=0.5, interpolation='linear', numeric_only=True, closed='both') ### Parameter Description | Parameter | Type | Description | Default Value | | --- | --- | --- | --- | | q | float or array-like | Quantile values, ranging from 0 to 1. Can be a single value or a list of multiple values. | 0.5 | | interpolation | str | Interpolation method when the quantile lies between two values. Options: 'linear', 'lower', 'higher', 'nearest', 'midpoint'. | 'linear' | | numeric_only | bool | If True, only numeric data will be considered. | True | | closed | str | Used in DataFrames to determine interval closure. Not commonly used in Series. | 'both' | ### Return Value * **Return Type**: `float` or `Series` * **Description**: Returns the value at the specified quantile. If q is a single value, returns a float; if q is a list, returns a Series. * * * ## Examples Let's go through a series of examples from simple to complex to fully master the usage of `Series.quantile()`. ### Example 1: Basic Usage - Calculating Median The median is the 50% quantile, which is the most commonly used quantile. ## Example import pandas as pd # Create a Series with student scores scores = pd.Series([65,70,72,75,78,80,82,85,88,90,92,95]) print("Student Scores:") print(scores) print() # Calculate median (50% quantile) median_score = scores.quantile(0.5) print(f"Median: {median_score}") print(f"Using median() function: {scores.median()}") print() print("Analysis: 50% of students scored below or equal to 80 points.") **Output:** Student Scores:0 651 702 723 754 755 806 807 858 889 9010 9211 95 dtype: int64 Median: 80.0Median (using median() function): 80.0 **Code Explanation:** * `quantile(0.5)` is equivalent to `median()`. * The median splits the data into two halves, with 50% of the data less than or equal to the median. ### Example 2: Calculating Quartiles Quartiles divide the data into four equal parts: 25%, 50%, and 75%. ## Example import pandas as pd # Create a Series with employee incomes income = pd.Series([3000,3500,3800,4000,4200,4500,5000,5500,6000,8000,15000]) print("Employee Monthly Income Data (Yuan):") print(income) print() # Calculate three quartiles q1 = income.quantile(0.25)# First quartile (25%) q2 = income.quantile(0.50)# Second quartile / median (50%) q3 = income.quantile(0.75)# Third quartile (75%) print(f"First Quartile Q1 (25%): {q1} Yuan") print(f"Second Quartile Q2 (50%): {q2} Yuan") print(f"Third Quartile Q3 (75%): {q3} Yuan") print() # Calculate interquartile range (IQR) iqr = q3 - q1 print(f"Interquartile Range IQR: {iqr} Yuan") print() print("Analysis:") print("- 25% of employees earn below or equal to 4000 Yuan") print("- 50% of employees earn below or equal to 5000 Yuan") print("- 75% of employees earn below or equal to 6000 Yuan") print("- The larger the IQR, the more spread out the data is") **Output:** Employee Monthly Income Data (Yuan):1 30002 Below 38003 40004 42005 45006 50007 55008 60009 800010 15000 dtype: int64 Q1 (25% quantile): 4000.0 Yuan Q2 (50% quantile): 5000.0 Yuan Q3 (75% quantile): 6000.0 YuanInterquartile Range IQR = 6000 - 4000 = 2000 Yuan ### Example 3: Calculating Multiple Quantiles at Once Multiple quantiles can be calculated at once. ## Example import pandas as pd # Create data data = pd.Series([10,20,30,40,50,60,70,80,90,100]) print("Data:") print(data) print() # Calculate multiple quantiles percentiles = data.quantile([0,0.1,0.25,0.5,0.75,0.9,1.0]) print("Quantiles:") print(percentiles) print() # Quantiles can also be specified as percentage strings (only for single values) print(f"Using string '50%': {data.quantile('50%')}") print(f"Using string '0.5': {data.quantile(0.5)}") **Output:** Data:0 101 202 303 404 50Values: 605 706 807 908 100 dtype: int64 Multiple quantiles:0.00 10.00.10 19.00.25 32.50.50 50.00.75 67.50.90 81.01.00 100.0 dtype: float64 ### Example 4: Effect of the interpolation Parameter Different interpolation methods produce different results when the quantile lies between two values. ## Example import pandas as pd # Create a Series with 6 elements data = pd.Series([10,20,30,40,50,60]) print("Data:", data.values) print() # Calculate 30% quantile (between 20 and 30) # Position = (n-1) * q = 5 * 0.3 = 1.5 print("30% quantile using different interpolation methods:") linear = data.quantile(0.3, interpolation='linear') print(f"linear (linear interpolation, default): {linear}") lower = data.quantile(0.3, interpolation='lower') print(f"lower (take smaller value): {lower}") higher = data.quantile(0.3, interpolation='higher') print(f"higher (take larger value): {higher}") nearest = data.quantile(0.3, interpolation='nearest') print(f"nearest (take nearest value): {nearest}") midpoint = data.quantile(0.3, interpolation='midpoint') print(f"midpoint (take midpoint): {midpoint}") **Output:** Data: [10, 20, 30, 40, 50, 60]Position calculation: (n-1) * q = 5 * 0.3 = 1.5, indicating between 20 and 30 Different interpolation results: - linear (linear interpolation, default): 23.0 - lower (round down): 20.0 - higher (round up): 30.0 - nearest (nearest neighbor): 20.0 - midpoint (midpoint): 25.0 **Code Explanation:** * `interpolation='linear'`: Linear interpolation between two values, 20 + (30-20)*0.5 = 23. * `interpolation='lower'`: Take the smaller index value, i.e., 20. * `interpolation='higher'`: Take the larger index value, i.e., 30. * `interpolation='nearest'`: Take the value closest to the quantile position. * `interpolation='midpoint'`: Take the midpoint of the two values, i.e., (20+30)/2 = 25. ### Example 5: Using Quantiles to Identify Outliers The interquartile range (IQR) is often used to identify outliers in data. ## Example import pandas as pd # Create a Series with some outliers data = pd.Series([12,15,18,20,22,25,28,30,32,150]) print("Data (with outliers):") print(data) print() # Calculate quartiles q1 = data.quantile(0.25) q3 = data.quantile(0.75) iqr = q3 - q1 # Calculate outlier boundaries lower_bound = q1 - 1.5 * iqr upper_bound = q3 + 1.5 * iqr print(f"Q1 (25%): {q1}") print(f"Q3 (75%): {q3}") print(f"IQR: {iqr}") print() print(f"Normal lower bound: {lower_bound}") print(f"Normal upper bound: {upper_bound}") print() # Identify outliers outliers = data[(data upper_bound)] print(f"Outliers: {outliers.values}") print() print("Analysis: 150 is clearly an outlier, exceeding the upper bound.") **Output:** Data (with outliers):3 1504 225 256 287 308 329 150 dtype: int64 Q1 (25%): 18.75 Q3 (75%): 30.25 IQR = 11.5Normal lower bound: 1.5Normal upper bound: 47.5Outliers: 150Analysis: 150 clearly exceeds the normal range and is an outlier. * * * ## Notes * Quantile values range from 0 to 1. * Linear interpolation (linear) is used by default to compute quantiles. * When q is a list, the return value is a Series, not a single value. * Quantiles are useful for identifying outliers, commonly using the IQR rule (1.5 times the IQR). * For large datasets, quantile calculations are highly efficient. * * * ## Summary `Series.quantile()` is an essential function for analyzing data distributions. Its main features include: * Supports calculating any quantile (between 0 and 1). * Can calculate multiple quantiles at once. * Offers various interpolation methods to meet different needs. * Very useful for identifying outliers. In practical data analysis, quantiles are often used to understand data distribution shapes, compare datasets, and identify outliers. Combined with box plots, they provide a more intuitive visualization of data distribution. [ Pandas Common Functions](#)