A laboratory report gives a value of “<0.05 mg/L”. A student copies it into a spreadsheet as zero and proudly calculates an average. That seemingly tidy decision changes what the data say. “Less than the reporting limit” is not an observed zero concentration, and replacing it silently can distort comparisons and conclusions.
The expression <0.05 mg/L means the laboratory has reported the result below a specified threshold of 0.05 milligrams per litre according to its test and reporting convention. Such a result is often called left-censored: the exact numerical concentration was not reported at that level of confidence or quantification. The result should be preserved with its inequality symbol and its own reporting-limit information rather than casually converted to zero.
- Preserve the less-than sign, number and units: <0.05 mg/L, not 0 or 0.05.
- Identify the analyte, sample, method, reporting limit and any qualifying codes.
- Do not infer from “not detected” that the substance is physically absent.
- A reporting limit can change with the method, dilution, sample or time period.
- For sums, means and trends, censored data require an explicit statistical treatment, not an invisible guess.
- A health or legal conclusion requires the current applicable standard, correct sample matrix and qualified professional interpretation.
- In school science, explain what the data can and cannot show before turning them into a graph.
Why laboratories publish a less-than result
A measurement instrument does not always produce a trustworthy quantified answer for every tiny concentration. The analytical process has background signals, detection limits, quality checks, calibration constraints and other sources of uncertainty. Rather than publish an unjustifiably exact small number, a laboratory may report that the measured sample is below its selected reporting threshold.
The US Geological Survey’s National Water-Quality Laboratory distinguishes several reporting conventions and describes why very low results may be censored or qualified. Its reporting-censoring explanation states that reporting limits depend on analytical methods and can change over time. The USGS reporting-procedures report also describes estimated low-concentration values and the responsibilities involved in interpretation.
A lab report is not merely a row of numbers. It is a communication about how far evidence supports a quantitative claim. A visible inequality warns the reader that ordinary arithmetic may not be appropriate without additional assumptions.
Three statements that sound similar but are not equivalent
“Zero milligrams per litre”
This would be a numerical value of zero under a specified measurement or reporting context. The number zero should not be manufactured simply because a method could not reliably report a small positive amount. A reported zero, if present, also needs its measurement definition and rounding rules understood.
“Less than 0.05 mg/L”
This says the report places the result below that level according to the laboratory’s convention. It does not say whether the true amount is absent, extremely small or near the threshold; method uncertainty and report qualifications matter. In a beginner exercise one might treat the listed figure as a boundary for illustrative calculations, but that is a teaching assumption, not a universal physical guarantee.
“Not tested” or “result missing”
These describe a different information state. A blank cell might mean the sample was never collected, the equipment failed, the lab did not run that analyte or the file omitted a result. None is the same as a valid below-limit report. Ask for the data dictionary or sample report before assigning meaning to an empty cell.
Learner diagnostic: read the symbol before calculating
Give the class four invented result cards: A, 0.00 mg/L; B, <0.05 mg/L; C, 0.08 mg/L; D, “not analysed”. Ask which can be entered as the numerical values shown without discarding meaning. Only C is straightforward as a quantified positive laboratory result in this simplified exercise. A still needs clarification about rounding and lab convention; B is censored; D is missing rather than a zero.
If learners treat B and D as interchangeable, start with language and evidence rather than statistics. If they understand the difference but still put zero into a spreadsheet, teach data types and column design. A good diagnostic asks what reason produced the wrong action; an incorrect mean is only the visible end of the misunderstanding.
Worked example 1: what can we say about an average?
Consider a fictional three-sample classroom dataset for one dissolved substance: Sample 1 is <0.05 mg/L, Sample 2 is 0.08 mg/L, and Sample 3 is 0.12 mg/L. A student writes (0 + 0.08 + 0.12) ÷ 3 = 0.0667 mg/L and labels it “the measured mean”. That is not justified: the first reported result was not an observed zero.
For a deliberately simplified interval demonstration, assume every true concentration is non-negative, the two displayed numeric readings are taken as exact for arithmetic purposes, and the first concentration lies somewhere from zero up to but not including 0.05 mg/L. Under those illustrative assumptions, the minimum possible total is 0 + 0.08 + 0.12 = 0.20 mg/L as a sum of concentrations, and its mean is 0.20 ÷ 3 = 0.0667 mg/L approximately.
The total for those three concentrations would be below 0.05 + 0.08 + 0.12 = 0.25 mg/L as a sum, giving a mean below 0.25 ÷ 3 = 0.0833 mg/L approximately. Therefore the unknown mean is in an illustrative range from about 0.0667 to below about 0.0833 mg/L. A single precise “measured mean” is not established from the displayed values.
Be careful: adding concentrations from different samples produces an intermediate arithmetic sum, not the concentration of a real mixed sample. The exercise demonstrates bounds on an arithmetic average, not a regulatory or environmental assessment. Actual laboratory readings also have uncertainties, so these are not certified bounds on true physical concentrations. They are a transparent mathematics lesson about incomplete numerical information.
Worked example 2: two reporting limits can change the story
A student compares fictional Test A from an older exercise, reported as <0.10 mg/L, with later Test B reported as <0.02 mg/L. Is this proof that the concentration fell by 80%? No. Both entries are below their respective reporting limits; neither supplies a quantified concentration. Even if the reporting limit became five times smaller, the actual concentration may or may not have changed.
The better conclusion reads: “The later report used or achieved a lower stated reporting threshold; neither value alone establishes the direction or size of any change in the underlying concentration.” This makes the difference between improvement in measurement capability and improvement in the system being measured. In research, confusing those can create a false trend.
Worked example 3: count censored records without inventing values
Consider five fictitious results for the same analyte: <0.05, 0.07, <0.05, 0.09 and 0.11 mg/L. Two of five records are censored under the stated reporting convention. The censored-record fraction is 2 ÷ 5 = 40%. What may we conclude? 40% of those records were reported with a less-than result at 0.05 mg/L.
We cannot conclude that 40% of all water samples everywhere have zero of the substance, or that the average concentration is known exactly. This is a count of reporting categories in a five-record dataset. It is often a genuinely useful descriptive statistic because it respects the data as supplied.
How to save these results correctly in a spreadsheet
A reliable classroom table separates the representation from the numeric threshold. Use columns such as sample ID; analyte; reported text; qualifier; reporting limit (mg/L); reported numeric result (mg/L); method; notes. For a below-limit record, keep “<0.05” in reported text and the qualifier “<”; store 0.05 as the reporting-limit field and leave the independently quantified-result field empty or specially encoded as specified by the dataset’s schema.
Avoid hiding an arbitrary substitution inside a formula cell. If a statistical method later requires handling censored values, document the method, its assumptions and its limitations in a separate analysis column. One analytical workflow might use specialized censored-data techniques; another may report detection frequency only. The correct choice depends on the scientific question, sample size and applicable guidance.
This is an ideal place to teach the difference between raw data and derived data. The original reported result is evidence and should not be overwritten merely to make charts easier. Create a derived column if needed, and label any transformation openly.
Why not always substitute half the reporting limit?
Replacing <0.05 mg/L by 0.025 mg/L is a familiar shortcut in some analyses, but it is still an assumption, not a measurement. It can bias an average or a trend when many results are censored, when thresholds vary, or when the data distribution is skewed. Some specialized protocols allow particular substitution methods under carefully stated conditions. The key educational rule is never make that choice silently or universally.
The US Environmental Protection Agency has published guidance on handling concentrations near detection limits in risk assessments discussing several distinct methods and the conditions in which they may be appropriate. Such guidance reinforces why a student should not treat the arithmetic convenience of one substitute value as a scientific truth.
A practice ladder that builds independent checking
Guided practice: read before you calculate
Present three labels on a board: “<0.2 µg/L”, “0.2 µg/L” and “not measured”. Ask learners to underline the unit, circle the comparison sign and identify the absent value. Only one is an ordinary stated numerical reading. Note that µg/L (micrograms per litre) is a different unit from mg/L (milligrams per litre).
Supported practice: change the unit correctly
Convert the reporting limit 0.05 mg/L to micrograms per litre. Since 1 mg = 1000 µg, 0.05 × 1000 = 50 µg/L. The full censored entry would become <50 µg/L, not 50 µg/L as an exact observation. The inequality survives the unit conversion.
Independent practice: critique the conclusion
A class report states, “All three samples were clean because the values were <0.1 mg/L.” Ask for a careful rewrite. A possible answer: “For the tested substance and method, all three laboratory reports were below their stated reporting threshold of 0.1 mg/L. These results alone do not show whether the water meets every relevant health or legal criterion.” Credit answers that name the analyte, method, scope and limitation.
Common misconceptions and why they persist
- “Non-detect means zero.” It can reflect a threshold or reporting convention, not physical proof of absence.
- “<0.05 means exactly 0.05.” The less-than sign explicitly prevents reading the number as an exact reported concentration.
- “A smaller reporting limit means cleaner samples.” It may reflect a more sensitive or different method.
- “Every blank is a non-detect.” Missing results require their own explanation.
- “If a spreadsheet requires a number, zero is a harmless placeholder.” Silent placeholders alter statistics and can create a false scientific claim.
- “No detected substance means every safety standard is met.” That conclusion needs the right contaminant list, relevant standards, sampling and professional assessment.
What parents, teachers and researchers can do
Parents do not need specialised lab equipment. They can ask a student to read a hypothetical report and describe the sign, units, threshold and one limitation. The child should be able to say “We do not know the exact value from this cell” without embarrassment. Knowing when data are insufficient is intellectual progress.
Teachers can use the same three-sample problem twice: first with the less-than sign visible and second with the first entry incorrectly replaced by zero. Let students compare the claims that follow. Assess their ability to preserve the raw record, distinguish assumptions from observations and state an honest conclusion. Do not reward a superficially precise answer that is unsupported.
In longer projects, compare this lesson with checking whether a school project conclusion is supported by its graph and distinguishing numerical display precision from measurement accuracy. Both help learners resist false precision.
Frequently asked questions
Can a “<” result be included in a graph?
Yes, if the graph or table clearly indicates the censorship/threshold and does not invent an exact point value. The best display depends on the question, number of censored results and intended audience. A plot may show the limit marker or use a specialized censored-data visualization.
Is “below detection” the same as “below quantification”?
Not necessarily. Laboratories distinguish detection and reliable quantification thresholds; some small detected values may be reported as estimated rather than as censored. Read the lab’s defined codes and method rather than assuming all “limits” mean the same thing.
Is the result <0.05 mg/L safe or unsafe?
The result alone cannot answer that. Safety or compliance depends on the substance, relevant health-based or legal threshold, sample type, test validity, time and circumstances. For an actual safety concern, consult the responsible authority or qualified practitioner.
How do I compare 0.05 mg/L with 50 µg/L?
They express the same concentration threshold because one milligram equals one thousand micrograms. Convert before comparing, and preserve any “less than” qualifier.
Can I calculate an exact mean if one value is reported with “<”?
Not from the displayed values alone. You may calculate a statistic under explicit assumptions or use an appropriate censored-data method, but the result must be labelled accordingly. Do not call an assumed substitution a direct measurement.
Learning to respect an honest limit
A good education teaches students to extract everything a result can support, without extracting an imaginary extra decimal. “I cannot conclude the exact mean from this report” can be the most accurate sentence in a scientific discussion. That precision in interpretation transfers directly into spreadsheets, homework, journalism, engineering and public decisions.
For further exercises in diagnosis-first learning and evidence checking, visit the eduKate Education Hub and the Secondary 1 Mathematics small-group teaching reference.
Primary references: USGS, Modification to Data Censoring; USGS, New Reporting Procedures; and US EPA, Regional Guidance on Concentration Data Near Detection Limits. All numerical datasets in the exercises are fabricated for teaching, not actual laboratory observations.