PSLE Science Reality Lab Vol No.127 | “>100” — Does That Mean the Result Is Exactly 100?

PSLE-SCI-REALITY-0127

Wait, What? “Greater Than 100” Is Not the Number 100

A public data table contains three results:

Sample	Reported result
A	42
B	78
C	>100

A graph-maker replaces “>100” with a bar of exactly 100 and labels Sample C as 100.

That is not what the report said.

The symbol “>100” means the result is known to be above 100 under the reporting system used. The actual value may be 101, 130, 500 or another value beyond that boundary. The report has preserved a lower bound, not an exact measurement.

This is called a form of right-censoring in data analysis: the observation is present, but the exact value beyond an upper reporting limit is not available in the ordinary form.

The Reality Lab learner job is not to master statistics terminology. It is to protect the scientific meaning of a symbol when data move from a laboratory table into a chart, headline or comparison.

Quick Answer

Read the comparison sign before the number.
Ask what caused the upper reporting boundary: instrument range, dilution limit, counting limit or another method condition.
Do not replace “>100” with exactly 100 unless the scientific purpose explicitly justifies a bounded substitution—and never pretend the substitution is the original measurement.
Be careful when ranking or averaging censored values because the unknown amount beyond the limit matters.
Keep the conclusion at the level the evidence supports: Sample C is above 100, not exactly 100.

The Exact Learner Job This Page Owns

This page owns one evidence-transfer problem: evaluating a table, chart, dashboard or claim in which an upper-censored result such as “>100” is silently converted into an exact value.

It does not replace canonical owners for measurement range, graph reading, detection/reporting limits or missing data. It applies those skills to a specific real-world scientific communication object: a greater-than result whose exact magnitude is not known from the report.

Original Reality Lab Case: The Counting Limit

This original case uses fictional Indicator Z. It is not copied from a medical, environmental or commercial report.

A field project counts visible colonies on test plates. Under its method, the team can count reliably up to 100 colonies on one plate. Above that, overlapping colonies make an exact count unreliable. The reporting rule is therefore:

0–100: report the counted number;
more than 100: report “>100” and follow the method’s next step if a more exact result is needed.

Plate	What is visible	Correct report
A	47 countable colonies	47
B	96 countable colonies	96
C	More than the reliable counting limit	>100

If the public chart redraws Plate C as exactly 100, it introduces information that the measurement did not provide. The original result says only that the value exceeds the upper reporting boundary.

Observed, Reported and Invented

Layer	Statement
Observed	The sample produced a signal beyond the method’s ordinary upper reporting range.
Reported	>100
Supported conclusion	The value is above 100 under the stated reporting system.
Invented precision	“The value is 100.”
Further unknown	How far above 100 the actual value lies.

Why Scientists Sometimes Report a Bound Instead of an Exact Number

Measurement methods have operating ranges. A sensor may saturate. A counting method may become too crowded. A laboratory may have a highest calibrated or validated range. A sample may need dilution before an exact value can be determined. In such cases, a careful report can preserve what is known without pretending to know more.

U.S. EPA guidance on water-quality data describes right-censored observations as values reported above a high-end quantitation limit. USGS publications similarly describe results as right censored when the actual value is greater than the reported bound.

That is scientifically honest. “>100” carries less numerical detail than “137”, but it carries more truth than an invented exact number.

The Comparison-Sign Check

A tiny symbol can change the entire meaning:

Report	Meaning
100	An exact reported numerical value under the method.
>100	The value is greater than 100; exact magnitude is not reported.
<100	The value is less than 100; exact magnitude may be unresolved.
≈100	Approximately 100; meaning depends on stated method/context.

Science reading is not merely reading digits. The symbols around the digits carry evidence.

The Representation Check: What Happens When a Chart Needs a Bar Height?

A graphing program wants a number. The dataset contains “>100”. The temptation is to enter 100 because the software cannot draw a greater-than sign as a bar height.

That convenience can change the meaning. Better options depend on the purpose:

show a bar reaching the upper plotting boundary with an arrow or “>100” label;
use a different symbol for censored observations;
plot a lower-bound marker rather than an ordinary exact point;
change the measurement method if the scientific question requires the actual magnitude.

The key is transparency. If a substitution is used for a specific calculation, the communication should state that it is an analytical choice, not the original observation.

Why Ranking Can Become Impossible

Suppose two samples are reported as:

Sample	Reported result
X	>100
Y	>100

Can you say X and Y are equal? No. X could be 110 and Y 400. Y could be 101 and X 900. The available report does not resolve the ranking.

Now suppose Sample Z is 150 from a method that can report exact values up to 500. Can you conclude Z is greater than X? Still not necessarily. X is only known to exceed 100; it might exceed 150.

This is a powerful scientific habit: do not rank quantities more finely than the evidence allows.

Why Averaging Can Become Misleading

A dataset contains 40, 60 and >100. A pupil replaces >100 with 100 and calculates an average of 66.7. Is that the true average? No. If the unknown value were 120, the mean would be 73.3. If it were 300, the mean would be 133.3.

The simple substitution may produce a number, but the number inherits the assumption. Analysts sometimes use specialised methods for censored data. A Primary learner only needs to understand the boundary: when one value is not known exactly, an exact-looking average can hide that uncertainty.

The Baseline Check: Why “Above the Limit” Is Not Automatically “Dangerous”

There are two very different kinds of “limit”:

a measurement/reporting limit, which describes what the method can quantify or report;
a safety, regulatory or performance limit, which describes a decision boundary.

If the method says “>100” because the instrument range ends at 100, that does not by itself mean 100 is a safety threshold. Conversely, a safety threshold can exist well inside the instrument’s measurement range.

Reality Lab keeps these owners separate so a technical reporting limit is not mistaken for a danger line.

Alternative Explanation: Dilution Could Recover the Exact Value

Sometimes a sample beyond the upper range can be diluted or measured with another validated method to bring the signal into range. That does not mean every “>100” result should automatically be re-run; it depends on the purpose of the investigation.

If the only question is whether a value exceeds 100, the censored result may already answer it. If the question is whether the value is 130 or 300, more measurement resolution is needed.

What Evidence Would Strengthen the Interpretation?

The report explains what the upper reporting limit means.
The reason for censoring is documented.
The chart preserves the greater-than symbol or an equivalent visual cue.
If exact magnitude matters, a validated follow-up measurement extends the range appropriately.
Any analytical substitution used for statistics is clearly described.
The conclusion distinguishes a measurement boundary from a safety or policy boundary.

What Would Weaken It?

“>100” is silently changed to 100.
Several censored values are treated as equal merely because they share the same reporting code.
A censored value is used in an exact average without acknowledging the assumption.
The highest reportable value is mistaken for the highest physically possible value.
The chart suggests a plateau at the reporting limit when the true process may continue increasing.
A technical upper range is presented as though it were a health or safety limit.

Worked Case 1: The Sensor Display Says “HIGH”

A sensor shows exact readings from 0 to 200, then displays HIGH above 200. A video changes HIGH to 200. That is the same mistake in a different costume. The device reports “above range”, not exactly the maximum display value.

Worked Case 2: The Too-Crowded Count

A plate can be counted reliably to 100 visible items. One sample is reported “>100”. Another is reported 88. The first is definitely greater than 100 under the method and therefore also greater than 88. But the exact difference between them is unknown.

Worked Case 3: Two Upper-Censored Samples

Sample A is >100 and Sample B is >100. A headline says, “Both samples contain the same amount.” That conclusion is unsupported. The available data only show that both exceed the same reporting boundary.

Worked Case 4: The Follow-Up Dilution

A first analysis gives >100. The sample is then appropriately diluted and re-analysed under a validated method, leading to an original-sample result of 340 after applying the dilution factor correctly. The second test adds information. It does not mean the first report was “wrong”; the first report correctly stated what was known at its range.

Tempting Reasoning That Fails

“>100 means 100.” It means the actual value is above 100.
“The instrument only reports to 100, so nothing can exceed 100.” A measurement range is not a physical ceiling.
“Two >100 results are equal.” They may differ greatly above the boundary.
“A >100 result is useless.” It can still answer a threshold question such as whether the value exceeds 100.
“Just use 100 in the graph because the software needs a number.” Software convenience is not a licence to change scientific meaning.

Model and Measurement Limits

The term right-censored can be used differently in different contexts, and laboratories may have specialised flags or procedures. This guide does not prescribe how professionals should analyse censored data. It teaches the public-reading habit that survives across systems: a bound is not an exact value.

Some methods can also report estimated values beyond normal limits, or may remeasure after dilution. Always read the method notes and data qualifiers rather than assuming every greater-than symbol was produced for the same reason.

How Far Can the Conclusion Travel?

“>100” can support conclusions that require only knowing the value exceeds 100. It cannot support an exact ranking against another value above 100, an exact difference, an exact average contribution, or an exact dose or concentration without additional evidence.

PSLE-Style Transfer Case

A light sensor reports exact brightness values up to 500 units. In very bright conditions it displays “>500”. Three locations are reported as 320, 470 and >500.

Question: Which conclusions are supported?

Reasoned answer: The third location is brighter than 500 units under the measurement system and therefore brighter than the locations reported as 320 and 470. Its exact brightness is not known from the “>500” report.

Explained Practice

Practice A: A table says >50. Can you plot it at exactly 50? Not without changing the meaning. It is a lower bound, not an exact 50.

Practice B: Two results are >50 and 45. Which is larger? The first is known to exceed 50 and therefore exceeds 45.

Practice C: Two results are >50 and 70. Which is larger? The available evidence does not necessarily tell you; the first could be 51 or 500.

Delayed Independent Return: The B-O-U-N-D Check

B — Boundary: What reporting limit was reached?
O — Operator: Is the symbol >, <, ≈ or an exact equals-style value?
U — Unknown: What part of the magnitude remains unresolved?
N — Needed: Does the scientific question require the exact value or only the bound?
D — Display: Did the chart preserve the bound without inventing precision?

Parent and Tutor Teaching Guide

Write three cards: “100”, “>100” and “exact value unknown but above 100”. Ask the learner which two cards mean the same thing. The answer is the second and third. Then ask the learner to invent three possible real values that fit “>100”.

Next, give the learner two censored values, >100 and >100, and ask whether equality is proven. This exposes a common mistake immediately: identical report codes do not imply identical underlying quantities.

Authoritative Sources

The current PSLE Science assessment objectives ask learners to interpret and analyse information, evaluate observations and methods, and communicate explanations. A greater-than sign in a scientific table is not decorative punctuation. It is part of the evidence.

The Quiet Return

Science sometimes knows a boundary before it knows an exact value.

That is not failure. It is honest resolution.

If the report says “greater than 100”, keep the greater-than sign alive all the way to your conclusion.

Small Group Tutorials