Class 11 Statistics Notes · GSEB

Absolute and Relative Measures

Absolute and Relative Measures — know which dispersion measures carry units and which coefficients free them for comparison. GSEB Class 11 Statistics notes with the measure family tree and paired-coefficient table.

Last updated: 5 Oct 2026

Notes

Absolute and Relative Measures

Words marked with a dotted underline carry the question they usually appear in — tap them to reveal it.

“Uncontrolled variation is the enemy of quality.”— Edward Deming

Absolute measure of dispersion

A measure that is expressed in the same statistical units as the data. Weights in kg produce a dispersion in kg; profits in lakh ₹ produce a dispersion in lakh ₹.

Relative measure of dispersion (coefficient)

A measure that is free from the unit of measurement — obtained by dividing an absolute measure by an appropriate average. Its value is called the coefficient of dispersion.

Why two kinds exist

An absolute measure tells you the size of the spread in the data's own unit. It answers “how big is the spread?” but never “which group is more variable?” once the two groups are measured differently. The relative measure answers exactly that second question.

One Family, Four Measures

The classification examiners ask for: dispersion splits into absolute and relative; the absolute side splits again into positional measures and measures built from deviations — each leaf carrying its own coefficient.

The two absolute branches

Positional — Range and Quartile Deviation take their value from where observations sit in the ordered data; no averaging of every value is involved.The measures based on deviations from the mean: Mean Deviation and Standard Deviation. These two use every observation, which is what makes them the preferred family.

Why Relative Measures Were Invented

Flip the switch below. In absolute mode the two spreads cannot be compared at all; in coefficient mode the same two numbers line up side by side.

One dataset, two ways of writing its spread

Group A — parcels at a courier hub

2.99 kg

spread in its own unit · mean = 35 kg

Group B — steel rods cut on a line

9.30 inch

spread in its own unit · mean = 62.5 inch

2.99 kg and 9.30 inch do not share a unit — subtracting them, or calling one “bigger”, would be meaningless.

When to reach for a coefficient

Relative measures are used for comparing two or more groups in terms of their variability — especially when the groups are measured in different units (weights in kg vs lengths in inch) or even the same unit at very different levels (a chai stall turning over ₹8,000 a day vs a restaurant turning over ₹2,00,000 a day).

Each Absolute Measure Has a Paired Coefficient

Absolute measures carry the data's unit; the paired coefficient divides it away.
Measure	Absolute (carries the unit)	Relative — coefficient (unit-free)
Range	R = x_H − x_L	(x_H − x_L)/(x_H + x_L)
Quartile Deviation	Qd = (Q3 − Q1)/2	(Q3 − Q1)/(Q3 + Q1)
Mean Deviation	MD = Σ\|x − x̄\|/n	MD/x̄
Standard Deviation	s = √(Σ(x − x̄)²/n)	s/x̄; CV = (s/x̄) × 100

The paired-coefficient idea

Range pairs with the coefficient of range · Quartile Deviation with the coefficient of QD · Mean Deviation with the coefficient of MD · Standard Deviation with the coefficient of SD — and the last one, written as a percentage, is the Coefficient of Variation (CV).Dividing by an appropriate average removes the unit: kilograms ÷ kilograms, inches ÷ inches — only a pure number survives.

Quick Reference

Positional

Range · Quartile Deviation

Deviation-based

Mean Deviation · Standard Deviation

Same unit as data

All four absolute measures

Named properly

The relative measure of any dispersion is called its coefficient of dispersion

Different units?

Only relative measures can compare groups measured in different units

Unit-free star

The unit-free measure is the Coefficient of Variation

Key Takeaways

Absolute measures are expressed in the same statistical units as the data; relative measures are free from the unit of measurement.
Every absolute measure has a paired coefficient — range → coefficient of range, QD → coefficient of QD, MD → coefficient of MD, SD → coefficient of SD and CV.
Relative measures exist for one job: comparing two or more groups in terms of their variability, especially across different units. So what: 2.99 kg and 9.30 inch cannot be ranked, but 8.54% and 14.88% can.
Positional measures (Range, QD) work off ordered data; deviation-based measures (MD, SD) work off distances from the mean.
The Coefficient of Variation is the unit-free measure — the one to quote whenever a spread has to travel outside its own dataset.