Quick Answer: Percentiles and Quartiles

What Are Percentiles and Quartiles?

Percentiles and Quartiles are descriptive statistics used to understand the position of values inside an ordered dataset. A percentile tells us the value below which a certain percentage of the data falls. For example, the 25th percentile is the value at or below which about 25% of observations fall. The 90th percentile is the value at or below which about 90% of observations fall.

Quartiles are special percentiles. The first quartile, or Q1, is the 25th percentile. The second quartile, or Q2, is the median or 50th percentile. The third quartile, or Q3, is the 75th percentile. Together, Q1, Q2 and Q3 provide a compact description of the distribution center and spread.

Percentiles and Quartiles are especially useful when a mean alone is not enough. A mean can be pulled by extreme values, while quartiles focus on ordered positions. This is why quartiles are central to box plot interpretation, five number summary, descriptive statistics and outlier checking.

Percentiles and Quartiles Formulas

There are several software-specific percentile calculation methods, so exact percentile values can sometimes differ slightly between SPSS, R, Python and Excel. However, the concept is the same: sort the values from smallest to largest, then identify the value at a selected cumulative position.

For this G3 example, Percentiles and Quartiles are interpreted as follows:

Dataset and Verified SPSS Results for Percentiles and Quartiles

This Percentiles and Quartiles guide uses the student performance dataset. The main variable is G3 final grade, and the supporting variables are G1, G2, age and absences. The SPSS output contains 649 valid cases and no missing values for these variables.

G3 Percentile Table for Percentiles and Quartiles

The SPSS percentile table gives a more detailed view of G3 than quartiles alone. Quartiles focus on the 25th, 50th and 75th percentiles, while the full percentile table also includes the 5th, 10th, 90th and 95th percentiles.

This table shows why Percentiles and Quartiles are useful for student grade interpretation. Instead of saying only “the mean is 11.91,” we can say that the central half of students scored between 10 and 14, and that the high-performing upper tail starts around 16 to 17.

Quartile Summary for Key Variables

The Percentiles and Quartiles summary below compares G1, G2, G3, age and absences. This comparison helps identify which variables are tightly concentrated and which variables have wider spread.

G3 Quartile Groups

SPSS can also create quartile groups. In this Percentiles and Quartiles analysis, G3 was ranked in ascending order and divided into four percentile groups. Because G3 has many tied grade values, the groups are not exactly 25% each. This is normal when the variable is discrete and many students share the same score.

G3 Mean and Range by Quartile Group

Python Chart-by-Chart Interpretation for Percentiles and Quartiles

The Python charts below explain Percentiles and Quartiles visually. Each chart should be read together with the SPSS table because the chart shows the pattern and the SPSS output provides the verified values.

R Chart-by-Chart Interpretation for Percentiles and Quartiles

The R charts repeat the same Percentiles and Quartiles analysis in a second workflow. This helps confirm that the interpretation is based on the data values, not on one software package.

SPSS Workflow for Percentiles and Quartiles

The SPSS output for this Percentiles and Quartiles guide includes percentile tables, quartile summaries, boxplot review, G3 quartile groups and G3 summary by quartile band.

Open the Percentiles and Quartiles SPSS Output PDF

SPSS Menu Steps

SPSS Syntax for Percentiles and Quartiles

* Percentiles and Quartiles - SPSS Syntax.

TITLE "Percentiles and Quartiles".

DATASET ACTIVATE PercentilesQuartilesData.

* Percentile table for G3.
FREQUENCIES VARIABLES=G3
  /FORMAT=NOTABLE
  /STATISTICS=MEAN MEDIAN MODE STDDEV VARIANCE SKEWNESS SESKEW KURTOSIS SEKURT RANGE MINIMUM MAXIMUM
  /PERCENTILES=5 10 25 50 75 90 95
  /ORDER=ANALYSIS.

* Quartile summary for key numeric variables.
FREQUENCIES VARIABLES=G1 G2 G3 age absences
  /FORMAT=NOTABLE
  /STATISTICS=MEAN MEDIAN STDDEV RANGE MINIMUM MAXIMUM
  /PERCENTILES=25 50 75
  /ORDER=ANALYSIS.

* Boxplot review.
EXAMINE VARIABLES=G1 G2 G3 age absences
  /PLOT=BOXPLOT
  /STATISTICS=DESCRIPTIVES
  /CINTERVAL=95
  /MISSING=LISTWISE
  /NOTOTAL.

* Create G3 quartile groups.
RANK VARIABLES=G3 (A)
  /NTILES(4)
  /PRINT=YES
  /TIES=MEAN
  /RANK INTO G3_quartile.

FREQUENCIES VARIABLES=G3_quartile
  /ORDER=ANALYSIS.

* Summary of G3 by quartile group.
MEANS TABLES=G3 BY G3_quartile
  /CELLS=COUNT MEAN MEDIAN STDDEV MIN MAX.

OUTPUT EXPORT
  /CONTENTS EXPORT=VISIBLE
  /PDF DOCUMENTFILE="Percentiles-and-Quartiles-SPSS-Output.pdf".

R, Python and Excel Workflows for Percentiles and Quartiles

Python Workflow for Percentiles and Quartiles

import pandas as pd
import numpy as np

df = pd.read_csv("dataset.csv")

numeric_vars = ["G1", "G2", "G3", "age", "absences"]
for col in numeric_vars:
    df[col] = pd.to_numeric(df[col], errors="coerce")

# Main G3 percentiles
g3 = df["G3"].dropna()

percentile_values = {
    "P5": np.percentile(g3, 5),
    "P10": np.percentile(g3, 10),
    "Q1 / P25": np.percentile(g3, 25),
    "Median / P50": np.percentile(g3, 50),
    "Q3 / P75": np.percentile(g3, 75),
    "P90": np.percentile(g3, 90),
    "P95": np.percentile(g3, 95)
}

q1 = np.percentile(g3, 25)
median = np.percentile(g3, 50)
q3 = np.percentile(g3, 75)
iqr = q3 - q1

print("G3 Percentiles and Quartiles")
print(percentile_values)
print("IQR:", iqr)

# Quartile summary for key variables
summary_rows = []
for col in numeric_vars:
    values = df[col].dropna()
    q1 = np.percentile(values, 25)
    q2 = np.percentile(values, 50)
    q3 = np.percentile(values, 75)
    summary_rows.append({
        "variable": col,
        "q1": q1,
        "median": q2,
        "q3": q3,
        "iqr": q3 - q1,
        "minimum": values.min(),
        "maximum": values.max()
    })

summary = pd.DataFrame(summary_rows)
print(summary)

R Workflow for Percentiles and Quartiles

# R: Percentiles and Quartiles

df <- read.csv("dataset.csv")

numeric_vars <- c("G1", "G2", "G3", "age", "absences")

# Main G3 percentiles
g3_percentiles <- quantile(
  df$G3,
  probs = c(.05, .10, .25, .50, .75, .90, .95),
  na.rm = TRUE
)

print(g3_percentiles)

q1 <- quantile(df$G3, .25, na.rm = TRUE)
median_g3 <- quantile(df$G3, .50, na.rm = TRUE)
q3 <- quantile(df$G3, .75, na.rm = TRUE)
iqr_g3 <- IQR(df$G3, na.rm = TRUE)

cat("Q1:", q1, "\n")
cat("Median:", median_g3, "\n")
cat("Q3:", q3, "\n")
cat("IQR:", iqr_g3, "\n")

# Quartile summary for key variables
quartile_summary <- data.frame(
  variable = numeric_vars,
  q1 = sapply(df[numeric_vars], quantile, probs = .25, na.rm = TRUE),
  median = sapply(df[numeric_vars], quantile, probs = .50, na.rm = TRUE),
  q3 = sapply(df[numeric_vars], quantile, probs = .75, na.rm = TRUE),
  iqr = sapply(df[numeric_vars], IQR, na.rm = TRUE)
)

print(quartile_summary)

Excel Workflow for Percentiles and Quartiles

Excel can calculate Percentiles and Quartiles quickly using built-in formulas. Put the G3 values in one column, for example cells A2:A650, then use these formulas:

APA and Report Writing for Percentiles and Quartiles

A clear Percentiles and Quartiles report should include the valid sample size, Q1, median, Q3, IQR, minimum and maximum. When interpreting student grades, it is also useful to include the 90th and 95th percentiles to describe the upper end of the distribution.

For a shorter report, write: “The middle 50% of G3 final grades fell between 10 and 14, with a median of 12.” This sentence gives the reader a practical understanding of the distribution without requiring a full technical table.

When to Use Percentiles and Quartiles

Percentiles and Quartiles are useful when the goal is to describe position, spread and ordered performance rather than only average performance. They are common in education, psychology, business analytics, survey analysis, health scores, ranking systems and outlier detection.

Downloads and Resources for Percentiles and Quartiles

Use the SPSS output PDF and chart links below to review the complete Percentiles and Quartiles analysis.

Related Guides for Percentiles and Quartiles

These related Salar Cafe guides support the interpretation of Percentiles and Quartiles, descriptive statistics, spread, normality and reporting.

External References

• UCI Machine Learning Repository: Student Performance Dataset
• IBM SPSS Statistics Documentation
• NumPy Percentile Documentation
• R Project for Statistical Computing
• Microsoft Excel Support