Quick Answer: Range Result

The verified SPSS output calculated Range for five variables: G1, G2, G3, age, and absences. Each variable had N = 649 valid cases and 0 missing cases. The largest range was for absences, where the minimum was 0, the maximum was 32, and the range was 32. The grade variables G1, G2, and G3 each had a range of 19, from a minimum of 0 to a maximum of 19. The age variable had the smallest range, from 15 to 22, giving a range of 7.

Hypothesis-style interpretation: Range is a descriptive statistic, not a significance test. It does not have a p-value and it does not test a null hypothesis. The practical decision is based on comparing minimum, maximum, and spread across variables. In this output, absences has the widest total spread, while age has the narrowest total spread. The grade variables have the same total range but different standard deviations, medians, skewness values, and interquartile ranges.

What Is Range?

Range is the distance between the smallest and largest value in a dataset. It is one of the simplest measures of dispersion. If the minimum and maximum values are far apart, the range is large. If they are close together, the range is small.

Range is often used at the beginning of a descriptive analysis because it quickly shows the total span of the observed data. For example, in this SPSS output, absences has a minimum of 0 and a maximum of 32, so its range is 32. This immediately tells us that the absence variable covers a much wider raw span than age, which has a range of only 7.

However, range does not tell us how the values are distributed between the minimum and maximum. Two variables can have the same range but very different shapes. In this example, G1, G2, and G3 all have a range of 19, but their means, standard deviations, medians, skewness, kurtosis, and interquartile ranges are not identical. Therefore, range should be used with other descriptive statistics.

Range Formula

The formula for range is direct:

For the G3 final grade variable, the SPSS output reports:

For the absences variable, the SPSS output reports:

For the age variable, the SPSS output reports:

Range Decision Logic

Range is not a hypothesis test. It does not produce a test statistic, p-value, confidence interval, or reject/fail-to-reject decision. Instead, range is a descriptive measure used to compare total observed spread.

Dataset and Variables Used

The worked example uses student performance variables. The variables included in the SPSS range output are G1, G2, G3, age, and absences. The range is especially useful here because the variables are measured on different scales. Grades run from 0 to 19, age runs from 15 to 22, and absences runs from 0 to 32.

For broader descriptive context, connect range with five-number summary, box plot interpretation, histogram interpretation, coefficient of variation, and standard deviation.

Verified SPSS Output Interpretation

The SPSS output provides the range, minimum, maximum, mean, median, standard deviation, variance, interquartile range, skewness, and kurtosis for the selected variables. The most important values for range interpretation are the minimum, maximum, and range rows.

SPSS Range Table

SPSS Detailed Spread Context

SPSS G3 Range by Sex

Both female and male groups have the same G3 range of 19, because both groups include scores from 0 to 19. However, the group means and standard deviations differ. Female students have a higher mean G3 score, while male students have a slightly larger standard deviation. This shows why range alone is not enough for group comparison.

SPSS G3 Range Bands

Python Chart-by-Chart Interpretation

The Python charts show the Range analysis visually. They include a distribution with minimum and maximum, a range comparison chart, minimum-maximum intervals, and group range comparison.

Python Chart 1: Distribution with Minimum and Maximum

This chart shows how the range is created from the two endpoints of the distribution. The minimum and maximum values define the full observed span of the variable. For G3, the minimum is 0 and the maximum is 19, so the range is 19. The chart helps readers see that range does not depend on the center of the distribution. It depends only on the lowest and highest observed values.

The distribution view is useful because it also reminds us of the limitation of range. Even if most observations are concentrated near the middle, the range is still determined by the endpoints. Therefore, a distribution chart should be read together with the range value.

Python Chart 2: Range Comparison

This chart compares range values across variables. Absences has the largest range at 32. G1, G2, and G3 each have a range of 19. Age has the smallest range at 7. The chart makes the main result very clear: absence counts cover the widest raw span in the dataset.

The comparison chart also shows why variable scale matters. A range of 32 absences is not directly the same kind of measurement as a range of 19 grade points. Therefore, when comparing variables measured on different scales, range should be interpreted carefully and supported with standardized or relative spread measures when needed.

Python Chart 3: Minimum Maximum Intervals

This chart displays the range as an interval from minimum to maximum. It is one of the best ways to explain range visually because the entire line represents the full observed span. For grade variables, the interval runs from 0 to 19. For age, the interval runs from 15 to 22. For absences, the interval runs from 0 to 32.

The interval chart helps readers understand why age has a small range even though it has meaningful variation. Age is naturally restricted in this student dataset. Absences, on the other hand, has a long maximum endpoint, which creates the widest interval.

Python Chart 4: Group Range Comparison

This chart compares G3 range for female and male students. SPSS shows that both groups have a minimum of 0, a maximum of 19, and a range of 19. Therefore, the total observed grade span is the same for both groups.

However, the same range does not mean the two groups have identical distributions. Female students have a mean G3 of 12.25, while male students have a mean G3 of 11.41. Male students have a slightly larger standard deviation. This chart teaches an important point: group range can be equal even when group averages and distributions differ.

R Chart-by-Chart Validation

The R charts validate the same Range interpretation using a separate software workflow. The R figures match the Python and SPSS conclusion: absences has the widest total range, age has the narrowest range, and G1, G2, and G3 have equal grade ranges.

R Chart 1: Distribution with Minimum and Maximum

The R distribution chart confirms that range is based on endpoints. The minimum and maximum values define the observed span, while the histogram shows how the values are distributed within that span. This validates the Python interpretation.

R Chart 2: Range Comparison

The R range comparison confirms the same ranking: absences has range 32, G1/G2/G3 have range 19, and age has range 7. This validates that the range calculation is consistent across software.

R Chart 3: Minimum Maximum Intervals

The R interval chart confirms the minimum-to-maximum spans. The grade variables share the same endpoint interval, age is tightly bounded, and absences stretches the farthest. This is a clear visual explanation of the range formula.

R Chart 4: Group Range Comparison

The R group comparison confirms that female and male students have the same G3 range of 19. This validates the SPSS group range output and shows that range equality does not necessarily mean mean equality or identical distribution shape.

SPSS, R, Python and Excel Workflows for Range

The Range workflow is simple in all major software. The key steps are to calculate the minimum, calculate the maximum, subtract the minimum from the maximum, and then interpret the result with other descriptive statistics.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Code Blocks for Range

SPSS Syntax for Range

* Range analysis in SPSS.
* Variables: G1 G2 G3 age absences.

TITLE "Range Analysis".

FREQUENCIES VARIABLES=G1 G2 G3 age absences
  /FORMAT=NOTABLE
  /STATISTICS=MEAN MEDIAN STDDEV VARIANCE RANGE MINIMUM MAXIMUM.

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

SORT CASES BY sex.
SPLIT FILE LAYERED BY sex.

FREQUENCIES VARIABLES=G3
  /FORMAT=NOTABLE
  /STATISTICS=MEAN MEDIAN STDDEV RANGE MINIMUM MAXIMUM.

SPLIT FILE OFF.

RANK VARIABLES=G3 (A)
  /NTILES(4)
  /PRINT=YES
  /TIES=MEAN
  /RANK INTO G3_range_band.

MEANS TABLES=G3 BY G3_range_band
  /CELLS=COUNT MEAN STDDEV MIN MAX.

OUTPUT EXPORT
  /CONTENTS EXPORT=VISIBLE
  /PDF DOCUMENTFILE="Range-SPSS-Output.pdf".

Python Code for Range

import pandas as pd

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

variables = ["G1", "G2", "G3", "age", "absences"]

rows = []
for var in variables:
    x = pd.to_numeric(df[var], errors="coerce").dropna()
    rows.append({
        "variable": var,
        "n": len(x),
        "mean": x.mean(),
        "median": x.median(),
        "std": x.std(ddof=1),
        "minimum": x.min(),
        "maximum": x.max(),
        "range": x.max() - x.min(),
        "iqr": x.quantile(0.75) - x.quantile(0.25)
    })

range_table = pd.DataFrame(rows)
print(range_table)

# Group range for G3 by sex
group_range = (
    df.assign(G3=pd.to_numeric(df["G3"], errors="coerce"))
      .dropna(subset=["G3"])
      .groupby("sex")["G3"]
      .agg(n="count", mean="mean", median="median", std="std", minimum="min", maximum="max")
      .reset_index()
)

group_range["range"] = group_range["maximum"] - group_range["minimum"]
print(group_range)

R Code for Range

# Range analysis in R

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

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

rows <- list()

for(v in variables){
  x <- as.numeric(df[[v]])
  x <- x[!is.na(x)]

  rows[[v]] <- data.frame(
    variable = v,
    n = length(x),
    mean = mean(x),
    median = median(x),
    sd = sd(x),
    minimum = min(x),
    maximum = max(x),
    range = max(x) - min(x),
    iqr = IQR(x)
  )
}

range_table <- do.call(rbind, rows)
print(range_table)

# Group range for G3 by sex
group_rows <- list()

for(g in unique(df$sex)){
  x <- as.numeric(df$G3[df$sex == g])
  x <- x[!is.na(x)]

  group_rows[[as.character(g)]] <- data.frame(
    group = g,
    n = length(x),
    mean = mean(x),
    median = median(x),
    sd = sd(x),
    minimum = min(x),
    maximum = max(x),
    range = max(x) - min(x)
  )
}

group_table <- do.call(rbind, group_rows)
print(group_table)

Excel Formulas for Range

Assume values are in A2:A650.

Minimum:
=MIN(A2:A650)

Maximum:
=MAX(A2:A650)

Range:
=MAX(A2:A650)-MIN(A2:A650)

Mean:
=AVERAGE(A2:A650)

Median:
=MEDIAN(A2:A650)

Standard deviation:
=STDEV.S(A2:A650)

Interquartile range:
=QUARTILE.INC(A2:A650,3)-QUARTILE.INC(A2:A650,1)

Group minimum for female group:
=MINIFS(G3_range, sex_range, "F")

Group maximum for female group:
=MAXIFS(G3_range, sex_range, "F")

Group range for female group:
=MAXIFS(G3_range, sex_range, "F")-MINIFS(G3_range, sex_range, "F")

Interpretation:
A larger range means a wider distance between the lowest and highest observed value.
Range should be interpreted with IQR, standard deviation, histogram and boxplot.

APA Reporting Wording for Range

When reporting range, include the minimum, maximum, range value, sample size, and a short interpretation. If comparing groups, report group-specific minimums, maximums, ranges, and means.

APA-Style Full-Sample Report

APA-Style Group Range Report

Student-Friendly Report Example

Common Mistakes in Range Interpretation

When to Use Range

Use Range when you need a quick, easy-to-explain measure of total observed spread. It is especially helpful in introductory descriptive statistics, data screening, dashboard summaries, and first-pass variable comparison.

For fuller interpretation, compare range with descriptive statistics, five-number summary, histogram interpretation, box plot interpretation, coefficient of variation, and effect size.

Downloads and Resources for Range

The resources below include the SPSS output PDF, Python charts, and R validation charts used in this guide.

Related Statistical Guides

Use these related guides to connect Range with descriptive statistics, spread, distribution shape, normality checks, confidence intervals, and reporting.