Box Plot Interpretation: How to Read Box Plots with R, Python, SPSS and Excel

R Validation Charts for Box Plot Interpretation

The R workflow produced matching validation charts. These R charts are useful because they confirm that the same box-plot interpretation appears outside Python and SPSS.

How to Run Box Plot Interpretation in SPSS, R, Python and Excel

Box Plot Interpretation in Python

Python can calculate quartiles, fences and outlier counts and then generate publication-ready box plots. This code uses the existing cleaned dataset file and creates output folders inside the correct topic folder.

import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

base_dir = r"D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides"
topic_dir = os.path.join(base_dir, "Box Plot Interpretation")
python_dir = os.path.join(topic_dir, "Python")
os.makedirs(python_dir, exist_ok=True)

input_csv = os.path.join(base_dir, "spss_ready_data.csv")
df = pd.read_csv(input_csv)

required = ["G1", "G2", "G3", "absences", "school", "sex", "studytime", "failures"]
missing = [c for c in required if c not in df.columns]
if missing:
    raise ValueError(f"Missing required columns: {missing}")

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

df["case_id"] = np.arange(1, len(df) + 1)

g3 = df["G3"].dropna()
q1 = g3.quantile(0.25)
median = g3.quantile(0.50)
q3 = g3.quantile(0.75)
iqr = q3 - q1
lower_fence = q1 - 1.5 * iqr
upper_fence = q3 + 1.5 * iqr
outlier_mask = (df["G3"] < lower_fence) | (df["G3"] > upper_fence)

summary = {
    "n": int(g3.count()),
    "q1": q1,
    "median": median,
    "q3": q3,
    "iqr": iqr,
    "lower_fence": lower_fence,
    "upper_fence": upper_fence,
    "outlier_count": int(outlier_mask.sum()),
    "outlier_percent": float(outlier_mask.mean() * 100)
}

print(summary)

pd.DataFrame([summary]).to_csv(
    os.path.join(python_dir, "box_plot_g3_summary.csv"),
    index=False
)

plt.figure(figsize=(12, 7))
plt.boxplot(g3, labels=["G3 final grade"], showmeans=True)
plt.title("Box Plot Interpretation: G3 Final Grade")
plt.ylabel("Final grade")
plt.grid(axis="y", alpha=0.25)
plt.tight_layout()
plt.savefig(os.path.join(python_dir, "chart_01_python_box_plot_g3_final_grade.png"), dpi=300)
plt.close()

Box Plot Interpretation in R

R is excellent for side-by-side box plots and grouped box plots. The workflow below reads the same cleaned CSV file and saves R output inside the correct topic folder.

library(tidyverse)

base_dir <- "D:/DATA ANALYSIS/A Basic Descriptive Statistics Guides"
topic_dir <- file.path(base_dir, "Box Plot Interpretation")
r_dir <- file.path(topic_dir, "R")
dir.create(r_dir, showWarnings = FALSE, recursive = TRUE)

data_file <- file.path(base_dir, "spss_ready_data.csv")
df <- read.csv(data_file, stringsAsFactors = FALSE)

df <- df %>%
  mutate(
    case_id = row_number(),
    G1 = as.numeric(G1),
    G2 = as.numeric(G2),
    G3 = as.numeric(G3),
    absences = as.numeric(absences),
    studytime = as.factor(studytime),
    failures = as.factor(failures),
    school = as.factor(school),
    sex = as.factor(sex)
  )

g3 <- df$G3

q1 <- quantile(g3, 0.25, na.rm = TRUE)
median_g3 <- median(g3, na.rm = TRUE)
q3 <- quantile(g3, 0.75, na.rm = TRUE)
iqr <- IQR(g3, na.rm = TRUE)
lower_fence <- q1 - 1.5 * iqr
upper_fence <- q3 + 1.5 * iqr
outlier_count <- sum(g3 < lower_fence | g3 > upper_fence, na.rm = TRUE)

summary_table <- tibble(
  n = sum(!is.na(g3)),
  q1 = q1,
  median = median_g3,
  q3 = q3,
  iqr = iqr,
  lower_fence = lower_fence,
  upper_fence = upper_fence,
  outlier_count = outlier_count,
  outlier_percent = outlier_count / sum(!is.na(g3)) * 100
)

write.csv(summary_table, file.path(r_dir, "box_plot_g3_summary.csv"), row.names = FALSE)

p1 <- ggplot(df, aes(x = "G3 final grade", y = G3)) +
  geom_boxplot(outlier.shape = 16) +
  stat_summary(fun = mean, geom = "point", shape = 23, size = 3, fill = "white") +
  labs(
    title = "Box Plot Interpretation: G3 Final Grade",
    subtitle = "Box shows Q1, median, Q3, IQR, whiskers and outlier cases",
    x = "",
    y = "Final grade"
  ) +
  theme_minimal(base_size = 14)

ggsave(file.path(r_dir, "chart_01_r_box_plot_g3_final_grade.png"), p1, width = 12, height = 7, dpi = 300)

Box Plot Interpretation in SPSS

The corrected SPSS syntax uses the existing cleaned dataset and exports the corrected SPSS output PDF. The main correction is that school and sex are converted into numeric grouping variables before EXAMINE, and the G3 box-plot fences are added using verified values.

* ============================================================.
* Box Plot Interpretation - Corrected SPSS Syntax.
* Existing cleaned input file:
* D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\spss_ready_data.csv
* Correct output folder:
* D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation\SPSS
* ============================================================.

SET UNICODE=ON.
SET DECIMAL=DOT.
SET PRINTBACK=ON.
SET TNUMBERS=VALUES.
SET TVARS=LABELS.

HOST COMMAND=['cmd /c if not exist "D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation" mkdir "D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation"'].
HOST COMMAND=['cmd /c if not exist "D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation\SPSS" mkdir "D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation\SPSS"'].

GET DATA
 /TYPE=TXT
 /FILE="D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\spss_ready_data.csv"
 /ENCODING='UTF8'
 /DELCASE=LINE
 /DELIMITERS=","
 /QUALIFIER='"'
 /ARRANGEMENT=DELIMITED
 /FIRSTCASE=2
 /IMPORTCASE=ALL
 /VARIABLES=
 school A20
 sex A20
 age F8.2
 address A20
 famsize A20
 Pstatus A20
 Medu F8.2
 Fedu F8.2
 Mjob A30
 Fjob A30
 reason A30
 guardian A30
 traveltime F8.2
 studytime F8.2
 failures F8.2
 schoolsup A20
 famsup A20
 paid A20
 activities A20
 nursery A20
 higher A20
 internet A20
 romantic A20
 famrel F8.2
 freetime F8.2
 goout F8.2
 Dalc F8.2
 Walc F8.2
 health F8.2
 absences F8.2
 G1 F8.2
 G2 F8.2
 G3 F8.2.
CACHE.
EXECUTE.

DATASET NAME BoxPlotInterpretationClean WINDOW=FRONT.

COMPUTE case_id = $CASENUM.
FORMATS case_id (F8.0).
EXECUTE.

VARIABLE LABELS
 case_id "Case ID"
 school "School"
 sex "Sex"
 age "Student age"
 studytime "Weekly study time category"
 failures "Number of past class failures"
 absences "Number of school absences"
 G1 "First period grade"
 G2 "Second period grade"
 G3 "Final grade".

VALUE LABELS studytime
 1 "Less than 2 hours"
 2 "2 to 5 hours"
 3 "5 to 10 hours"
 4 "More than 10 hours".

VALUE LABELS failures
 0 "0 failures"
 1 "1 failure"
 2 "2 failures"
 3 "3 failures".
EXECUTE.

NUMERIC school_group sex_group (F1.0).

DO IF (RTRIM(school) = "GP").
 COMPUTE school_group = 1.
ELSE IF (RTRIM(school) = "MS").
 COMPUTE school_group = 2.
END IF.

DO IF (RTRIM(sex) = "F").
 COMPUTE sex_group = 1.
ELSE IF (RTRIM(sex) = "M").
 COMPUTE sex_group = 2.
END IF.

VALUE LABELS school_group
 1 "GP"
 2 "MS".

VALUE LABELS sex_group
 1 "Female"
 2 "Male".
EXECUTE.

COMPUTE numeric_missing_count = SUM(
 MISSING(G1),
 MISSING(G2),
 MISSING(G3),
 MISSING(absences),
 MISSING(studytime),
 MISSING(failures)
).

COMPUTE string_missing_count = SUM(
 MISSING(school),
 MISSING(sex)
).

COMPUTE complete_boxplot_case = (numeric_missing_count = 0 AND string_missing_count = 0).
EXECUTE.

FREQUENCIES VARIABLES=complete_boxplot_case numeric_missing_count string_missing_count
 /ORDER=ANALYSIS.

DESCRIPTIVES VARIABLES=G1 G2 G3 absences age studytime failures Medu Fedu
 /STATISTICS=MEAN STDDEV MIN MAX.

FREQUENCIES VARIABLES=G1 G2 G3 absences
 /STATISTICS=MEAN MEDIAN STDDEV MINIMUM MAXIMUM SKEWNESS SESKEW KURTOSIS SEKURT
 /PERCENTILES=25 50 75
 /ORDER=ANALYSIS.

EXAMINE VARIABLES=G1 G2 G3 absences
 /PLOT BOXPLOT STEMLEAF
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

EXAMINE VARIABLES=G3 BY school_group
 /PLOT BOXPLOT
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

EXAMINE VARIABLES=G3 BY sex_group
 /PLOT BOXPLOT
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

EXAMINE VARIABLES=G3 BY studytime
 /PLOT BOXPLOT
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

EXAMINE VARIABLES=G3 BY failures
 /PLOT BOXPLOT
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

EXAMINE VARIABLES=absences BY school_group
 /PLOT BOXPLOT
 /COMPARE GROUPS
 /STATISTICS DESCRIPTIVES EXTREME
 /CINTERVAL 95
 /MISSING LISTWISE
 /NOTOTAL.

COMPUTE g3_q1 = 10.
COMPUTE g3_median = 12.
COMPUTE g3_q3 = 14.
COMPUTE g3_iqr = g3_q3 - g3_q1.
COMPUTE g3_lower_fence = g3_q1 - (1.5 * g3_iqr).
COMPUTE g3_upper_fence = g3_q3 + (1.5 * g3_iqr).
COMPUTE g3_boxplot_outlier = (G3 < g3_lower_fence OR G3 > g3_upper_fence).
EXECUTE.

FREQUENCIES VARIABLES=g3_boxplot_outlier
 /ORDER=ANALYSIS.

DESCRIPTIVES VARIABLES=g3_q1 g3_median g3_q3 g3_iqr g3_lower_fence g3_upper_fence
 /STATISTICS=MEAN MIN MAX.

OUTPUT EXPORT
 /CONTENTS EXPORT=VISIBLE
 /PDF DOCUMENTFILE="D:\DATA ANALYSIS\A Basic Descriptive Statistics Guides\Box Plot Interpretation\SPSS\Box-Plot-Interpretation-SPSS-output-CORRECTED.pdf".

Box Plot Interpretation in Excel

Excel can create a box-and-whisker chart and calculate the same interpretation values manually. For a simple classroom or report workflow, Excel is enough for Q1, median, Q3, IQR and fences. For detailed output, SPSS, R or Python is better.

Example Excel formulas:

Q1:
=QUARTILE.INC(B2:B650,1)

Median:
=MEDIAN(B2:B650)

Q3:
=QUARTILE.INC(B2:B650,3)

IQR:
=Q3-Q1

Lower fence:
=Q1-1.5*IQR

Upper fence:
=Q3+1.5*IQR

Outlier flag:
=IF(OR(B2<Lower_Fence,B2>Upper_Fence),"Outlier","Not outlier")

How to Report Box Plot Interpretation Results

A strong box plot report should not simply say that a box plot was created. It should mention the median, quartiles, IQR, whiskers, fences and outlier candidates. If groups are compared, it should describe which group has the higher center, wider spread or more visible outliers.

Related Data Analysis Guides

After learning Box Plot Interpretation, continue with related guides that support descriptive statistics, assumption checking and regression diagnostics. For visual normality checking, use the Q-Q Plot Normality Check. For formal normality testing, use the Kolmogorov-Smirnov Test, DAgostino Pearson Test and Cramer von Mises Test. If box plots show unusual spread across groups, also check variance behavior with the Brown-Forsythe Test, Goldfeld-Quandt Test, Cochran C Test and Hartley F Max Test.

When Should You Use Box Plots?

Use box plots when you need a quick visual summary of a numeric variable or when you want to compare distributions across groups. Box plots are especially helpful when the dataset includes outliers, skewness, unequal spread or multiple categories.

Common Mistakes

1. Thinking a box-plot outlier is always wrong

A box-plot outlier is only unusual according to the 1.5 × IQR rule. It may be a real observation. In this example, low G3 scores are unusual but may still be valid student grades.

2. Ignoring the median

The median is one of the most important parts of a box plot. It tells where the middle of the distribution is located. In the G3 example, the median is 12.

3. Reading the box as the full range

The box is not the full range. It represents the middle 50% of the data. Whiskers and outlier points show values outside that middle range.

4. Comparing means only

Many charts focus on means, but box plots focus on medians and quartiles. The mean marker can be helpful, but the main interpretation should come from the median, IQR and whiskers.

5. Forgetting group sample sizes

Grouped box plots can look very different when sample sizes are unequal. A small group may have a less stable box shape than a larger group.

6. Using box plots as a replacement for formal tests

A box plot is a descriptive graph. It can suggest group differences, but it does not test whether those differences are statistically significant.

Download SPSS Output and Verification Files

The corrected SPSS output PDF verifies the clean data import, missing-value check, descriptive statistics, main box plots, grouped box plots, G3 fences and outlier count.

External References for Box Plot Interpretation and Data Analysis

This post uses verified SPSS, R and Python outputs together with external statistical references and software documentation. These resources help readers verify the dataset source, SPSS workflow, R workflow and Python visualization tools used in the box plot interpretation process.

• UCI Machine Learning Repository: Student Performance dataset
• IBM SPSS Statistics documentation
• The Comprehensive R Archive Network
• ggplot2 documentation
• Pandas documentation
• Matplotlib documentation
• Microsoft Excel support documentation