Mark Scaling Calculator

A paper comes out harder than intended and the marks need moving. The standard fix is a linear scaling: multiply and shift so the cohort lands on the mean and spread you wanted. What is usually left unsaid is that a bounded scale bites — push the mean high enough and the top of the class hits the ceiling, at which point you no longer get the mean you asked for. This does the scaling and reports the gap rather than hiding it.

Raw marks

Separated by commas or spaces. Order does not matter — the scaling never changes who is ahead of whom.

Target mean

Where you want the cohort centred after scaling, on the same scale as the raw marks.

Target spread

The standard deviation you want. A larger figure pulls the ends of the cohort further apart, which is what causes clipping.

Maximum mark

The top of the scale. Marks cannot be scaled beyond it, which is where the targets start to give way.

Your result will appear here.

What this generator does

Finds the multiplier and offset that would put the cohort on your target mean and spread, applies them to every mark, holds the results inside the scale, and then reports the mean and spread actually achieved rather than the ones requested.

How to use this tool

Paste the raw marks, separated by commas or spaces.
Set the mean and spread you want after scaling.
Set the maximum mark on the scale.
Read the scaled marks, and how close the result actually came to your targets.

Understanding the controls

Raw marks: Separated by commas or spaces. Order does not matter, since the scaling never changes who is ahead of whom.
Target mean: Where you want the cohort centred after scaling, on the same scale as the raw marks.
Target spread: The standard deviation you want. A larger figure pulls the ends of the cohort further apart, and that is what causes clipping.
Maximum mark: The top of the scale. Marks cannot be scaled beyond it, which is where the targets begin to give way.

Common use cases

Moderating a paper that turned out harder than intended
Bringing two classes onto a comparable scale
Seeing what a target mean does to the top of the cohort
Checking that a proposed scaling does not cap anyone
Explaining to a department why a scaling cannot always hit its target

How this generator works

There is exactly one linear transform taking a set of marks to a given mean and standard deviation: multiply by the ratio of the spreads, then shift so the means line up. Applying it is straightforward; the interesting part is the boundary. A mark scaled above the maximum has to be held at it, and every mark held that way pulls the achieved mean below the target and squeezes the achieved spread. Before display the achieved mean and spread are re-derived from the finished marks rather than assumed, every mark is confirmed to lie on the scale, the order of the cohort is checked to be unchanged, and wherever nothing was clipped the targets are confirmed genuinely met.

Randomness and fairness

Nothing here is random. A set of marks and a pair of targets give exactly one scaling, computed rather than fitted.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

Linear scaling preserves order but not gaps: it can widen the distance between two candidates who were a mark apart, which is a fairness question rather than an arithmetic one.
Clipping at the ends means the targets cannot always be met, and the page reports the gap rather than adjusting the targets to hide it.
Scaling cannot fix a paper that failed to discriminate. If everyone scored the same, no transform will separate them.
Awarding bodies use rank-based and statistical moderation methods well beyond a linear scaling, and this is not a substitute for them.

Privacy and your data

The scaling runs in your browser. No names are entered, and the marks you paste are never transmitted, stored or included in analytics.