Measures of Dispersion: JAMB Mathematics Questions, Answers & Notes

What Measures of Dispersion covers in the JAMB Mathematics syllabus

Measures of dispersion describe how spread out data is. The range = highest − lowest (simple but crude). The interquartile range (IQR) = Q₃ − Q₁ focuses on the middle 50%, and the semi-interquartile range is half of that. The variance is the average of the squared deviations from the mean, and the standard deviation = √variance — both use every value, so a small standard deviation means values cluster near the mean. Adding the same constant to every value leaves the spread unchanged; variance and standard deviation are never negative, and are 0 only when all values are equal.

For Measures of Dispersion, JAMB expects you to be able to:

• Calculate the range and interquartile range
• Understand variance and standard deviation and their relationship
• Interpret spread and the effect of adding a constant

Key facts & revision notes: Measures of Dispersion

These are the recurring points our Measures of Dispersion questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• Range = highest − lowest = 15 − 2 = 13.
• The range is a simple measure of how spread out the data is.
• All values are equal, so range = 20 − 20 = 0.
• The interquartile range (IQR) = upper quartile − lower quartile.
• Variance = (standard deviation)².
• Equivalently, standard deviation = √variance.
• Standard deviation = √variance = √25 = 5.
• The standard deviation is calculated from every value, unlike the range.
• A small standard deviation indicates values lie close to the mean.
• IQR = Q₃ − Q₁ = 20 − 12 = 8.
• Q₁ is the first quartile; 25% of the ordered data lies below it.
• Adding the same constant shifts all values equally, so the spread (standard deviation) is unchanged.
• Q₃ is the third quartile; 75% of the ordered data lies below it.
• Mean deviation is the average of the absolute differences between each value and the mean.
• A larger standard deviation means the values are more spread from the mean.
• The semi-interquartile range is half the interquartile range: (Q₃ − Q₁)/2.
• The range is the simplest measure — just highest minus lowest — but ignores the middle values.
• A standard deviation of 0 means there is no spread — every value equals the mean.
• Since it comes from squared deviations, variance is never negative (zero or positive).
• Range = highest − lowest.
• All values equal, so range = 7 − 7 = 0.
• IQR = Q₃ − Q₁ = 27 − 15 = 12.
• Standard deviation = √variance.
• Large standard deviation means high spread.

Worked examples

Three Measures of Dispersion questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Measures of Dispersion is tested in JAMB Mathematics

Our Measures of Dispersion bank holds 40 questions (12 easy, 22 medium, 6 hard). JAMB Mathematics typically returns to Measures of Dispersion year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Measures of Dispersion questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Measures of Dispersion. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Measures of Dispersion is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Measures of Dispersion

The errors that cost marks on Measures of Dispersion are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Measures of Dispersion actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Measures of Dispersion part of the JAMB Mathematics syllabus?

Yes. Measures of Dispersion is a recognised topic in the JAMB Mathematics syllabus, covering calculate the range and interquartile range. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Measures of Dispersion questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Measures of Dispersion questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Measures of Dispersion?

Measures of dispersion describe how spread out data is. The range = highest − lowest (simple but crude). The interquartile range (IQR) = Q₃ − Q₁ focuses on the middle 50%, and the semi-interquartile range is half of that. The variance is the average of the squared deviations from the mean, and the s…

How do I answer Measures of Dispersion questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Measures of Dispersion. Practising timed Measures of Dispersion questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Measures of Dispersion questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Measures of Dispersion questions free without signing up?

Right here — tap “Start Measures of Dispersion practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.