Does a bigger range mean a better or more consistent data set?

No. The range measures how spread out the data is — it is not a quality or size score. A bigger range means the values vary more, which is less consistent, not more. If Team A has a range of 4 and Team B has a range of 12, Team A is the more consistent team because its scores are bunched closer together. A smaller range means more consistent.

If you add the same number to every value, does the range change?

No — the range is unchanged. Adding the same amount to every value slides the whole data set along the number line, but the gap between the largest and smallest value stays the same. For example, 12, 7, 19, 4, 15 has a range of 19 − 4 = 15. Add 10 to every value to get 22, 17, 29, 14, 25: the new range is 29 − 14 = 15, still 15. The median rises by 10 (from 12 to 22) — the centre shifts — but the spread does not.

How do you decide which of two data sets is more consistent?

Compare the range alongside the mean. If two sets have the same mean, the one with the smaller range is more consistent because its values are closer together. For example, Set P (5, 8, 11, 8, 8) and Set Q (2, 14, 8, 6, 10) both have a mean of 8; P has a range of 6 and Q has a range of 12, so P is more consistent.

GCSE Maths Foundation · AQA · Averages & spread

Interpreting the range: a smaller range means more consistent, and a constant shift leaves the range unchanged

Spread questions trip students who read the range as a score for how “good” or “big” a data set is. Asked which team is more consistent, they pick the team with the bigger range — because bigger feels better. And when every value in a set is increased by the same amount, they assume the range grows too, because “the numbers got bigger.”

The thirty-second fix: the range (largest − smallest) measures spread; a smaller range means more consistent; and adding the same amount to every value shifts the centre but leaves the range unchanged.

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How to spot it in your own work

You said the team with the bigger range was more consistent — treating a bigger range as “better.”
You did not know that a smaller range means the data is more consistent.
You assumed that adding the same number to every value increases the range, when in fact the range is $\text{unchanged}$ .
You added the largest and smallest values ( $19 + 4$ ) instead of subtracting ( $19 - 4$ ) to find the range.

An exam question that triggers it

Here is the canonical AQA Foundation trigger (Jun23 P1 Q14 / Jun24 P1 Q9b shape):

Team A’s scores have a range of 4. Team B’s scores have a range of 12. Which team is more consistent?

The misconception answer is Team B — reading a bigger range as “better.” But the range measures spread, so a smaller range means the scores are closer together.

Team A’s range of $4$ is smaller than Team B’s $12$ , so Team A is more consistent.

Why students fall for this

The word “range” in everyday speech suggests variety or richness — “a wide range of choices” sounds like a good thing. Students carry that positive connotation into statistics and read a bigger range as “more” or “better,” rather than as “more spread out.”

The consistency direction is the inverse of this and is rarely made explicit: small spread = consistent. Because consistency is about results staying close to each other, it is the smaller range that signals it — the opposite of what “bigger is better” would predict.

The constant-shift error is structural: when every value increases, the largest and the smallest both increase by the same amount, so the gap between them — the range — is unchanged. Students who picture only “the numbers got bigger” miss that the two endpoints move together, leaving the spread fixed.

The fix: Range measures spread; smaller is more consistent; a shift leaves it unchanged

Range = largest − smallest, and it measures spread. For $12, 7, 19, 4, 15$ : range = $19 - 4 = 15$ . It is always a subtraction, never an addition.

A smaller range means more consistent. If Team A has a range of 4 and Team B a range of 12, Team A’s scores are bunched closer together, so Team A is more consistent. Bigger is not better — it is just more spread out.

Adding a constant to every value leaves the range unchanged. $12, 7, 19, 4, 15$ has range 15; add 10 to every value to get $22, 17, 29, 14, 25$ , range = $29 - 14 = 15$ — still 15. The mean and median rise by 10 (the centre shifts), but the spread does not.

Worked example

Two classes have the same mean mark of 16. Which is more consistent?

Find each range. Class A (12, 15, 18, 15, 20):
$20 - 12 = 8$
Class B (9, 22, 16, 18, 15):
$22 - 9 = 13$
Compare the spread (the means are equal). Class A’s range of 8 is smaller than Class B’s 13.
State the conclusion.
$\text{Class A is more consistent (smaller range)}$

The trap answer “Class B” treats the bigger range as better. A bigger range means more variation — the opposite of consistent.

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Common questions

Is the range a measure of average or of spread?: Spread. The mean, median, and mode are averages — they tell you the centre of the data. The range tells you how spread out the data is around that centre. They answer different questions, so a question asking for the range is not asking for an average.
Why does adding the same number to every value not change the range?: Because the largest and smallest values both increase by that same number, so the gap between them stays the same. For $12, 7, 19, 4, 15$ the range is 15; after adding 10 the set is $22, 17, 29, 14, 25$ and the range is still $29 - 14 = 15$ . The mean and median shift up by 10, but the spread is unchanged.
Two data sets have the same range — does that mean they are identical?: No. The range only uses the largest and smallest values, so two very different sets can share a range. For example, 1, 1, 1, 9 and 1, 5, 6, 9 both have a range of $9 - 1 = 8$ , but the data inside is quite different. The range measures the overall spread, not the detail of how the values are distributed.
How do I compare consistency when two sets have different means?: State both pieces: compare the means to describe who scored higher on average, then compare the ranges to describe who is more consistent. The smaller range is the more consistent — independently of which set has the higher mean. A full answer qualifies the comparison: “Set A has the higher mean, but Set B is more consistent because its range is smaller.”

Related misconceptions

Computing mean and median: why you must sort before finding the middleThe companion averages skill: the range is a measure of spread, while the mean and median are measures of centre — a question asking for one is not asking for the other.
Confusing statistical measures: why the range of 3, 8, 5, 12, 7 is 9, not the meanA related error: naming or computing the wrong measure entirely — giving the mean when asked for the range, or the mode when asked for the outlier.
Fraction of an amount: why 2/5 of 1020 is 408, not 40Another case where everyday intuition about a word overrides the precise mathematical operation the question demands.

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