Chemistry 化学

Examples of Discussing Outliers | When They May and May Not Be Excluded

An outlier is a value that deviates greatly from the trend of other values among multiple measurements or points on a graph.
In chemistry experiments, outliers may be found in titration values, absorbance, concentration, mass, pH, reaction rate, calibration curve measurement points, melting points, potentials, peak areas, and other measurements.
An outlier may simply be the result of a measurement error, or it may be important information indicating a change in experimental conditions or sample inhomogeneity.

The most important point when discussing outliers is not to treat them as values that can be excluded simply because they are inconvenient.
An outlier may be excluded when there is a reasonable reason, such as a clear abnormality during measurement, an operational error, a recording error, or an equipment malfunction.
On the other hand, it is not appropriate to exclude an outlier simply because it does not fit the regression line, is far from the mean, or makes the report results look poor.

This article explains, as examples of discussions that can be used in experimental reports on outliers, the meaning of outliers, when they may and may not be excluded, their effects on the mean and standard deviation, their effects on calibration curves and regression lines, the need for remeasurement, how to write about them in reports, causes of error, and points for improvement.

Note:
This article is a reference for discussing outliers obtained in basic chemistry experiments, analytical chemistry experiments, physical chemistry experiments, and materials chemistry experiments at universities and similar institutions.
For the actual criteria for excluding outliers, statistical tests, handling of remeasurements, and how to describe them in reports, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.

What Is an Outlier?

An outlier is a value that deviates greatly from the trend of other measurements.
If only one value among multiple measurements is extremely large or small, that value may be an outlier.
Also, when a calibration curve or regression line is created, a single point that deviates greatly from the line may be considered an outlier.

However, an outlier is not necessarily an “incorrect value.”
There may have been an abnormality in the experimental procedure, or it may contain important information, such as the sample itself being inhomogeneous, some reaction conditions being different, or an unexpected reaction having occurred.
When an outlier is found, it is important to first consider its cause.

Example Discussion:
Because only one of the measured values deviated greatly from the other values, this value may be an outlier.
Outliers may be caused by measurement errors or operational errors, but they may also reflect sample inhomogeneity or differences in measurement conditions.
Therefore, rather than simply excluding an outlier, it is necessary to first investigate its cause and then determine how it should be handled.

Main Items to Include in the Results

To discuss an outlier, it is necessary to organize not only the value considered to be an outlier, but also the other measured values, mean, standard deviation, regression line, measurement conditions, and operational records.
Comparing how the mean, standard deviation, correlation coefficient, and conclusion change when the outlier is included and when it is excluded makes it easier to explain the effect of the outlier.

Main Items to Include in the Results

  • All measured values
  • Value considered to be an outlier
  • Number of measurements
  • Mean
  • Standard deviation
  • Relative standard deviation
  • Results including the outlier
  • Results excluding the outlier
  • Operational records from the measurement in which the outlier occurred
  • Presence or absence of abnormalities during measurement
  • Whether remeasurement was performed
  • Effect on the regression line and correlation coefficient
  • Basis for exclusion if the value was excluded
  • Reason for not excluding the value if it was not excluded
  • Effect on the conclusion
  • Points for improvement

Example of How to Write the Results:
Of the five measured values, one was larger than the others and also deviated greatly from the mean.
Including this value increased the standard deviation, resulting in a lower evaluation of the reproducibility of the measurements as a whole.
However, because no clear operational error during measurement could be confirmed, the value was not readily excluded as an outlier and was instead discussed as a factor that increased the variation.

Main Causes of Outliers

Causes of outliers include errors in measurement procedures, errors in sample preparation, equipment malfunctions, instrument noise, sample inhomogeneity, deviations in reaction conditions, and recording errors.
For example, outliers may be caused by greatly exceeding the endpoint in titration, bubbles entering the cell during absorbance measurement, or spilling the sample during mass measurement.

When discussing an outlier, consider at which stage of the experiment an abnormality was likely to have occurred.
Organizing whether the problem occurred during sample preparation, reaction, separation, drying, measurement, calculation, or recording makes it easier to identify the cause specifically.

Cause Specific Example Effect on Results
Operational error Incorrect pipetting volume, exceeding the titration endpoint Measured value deviates greatly
Measurement error Bubbles in the cell, balance reading error Only a specific measured value becomes abnormal
Sample inhomogeneity Insufficient mixing, uneven distribution of precipitate Values vary depending on the sampling location
Recording error Incorrect digit entry, unit conversion error Calculated result deviates greatly

Example Discussion:
Possible causes of the outlier include insufficient mixing of the sample and an operational error during measurement.
In particular, if the sample is not homogeneous, the concentration or amount of components may differ depending on the portion sampled, resulting in a value that deviates greatly from the other measurements.
Therefore, when an outlier is observed, it is necessary to check not only the measurement procedure but also the sample preparation stage.

When an Outlier May Be Excluded

An outlier may be excluded when there is a clear reason to determine that the value is not a valid measurement corresponding to the purpose of the experiment.
Examples include spilling the sample, using the wrong pipetting volume, clearly exceeding the titration endpoint, having bubbles in the absorbance cell, receiving an instrument error, or recording the wrong digit.
In such cases, the measured value cannot be regarded as having been obtained under the same conditions, so exclusion may be considered.

However, when excluding a value, the reason must be clearly stated in the report.
If possible, it is preferable to confirm the result by remeasurement rather than excluding the outlier.
Showing how the mean, standard deviation, and regression line change before and after exclusion makes the decision more transparent.

Example Discussion:
During the measurement that produced the outlier, bubbles were observed in the cell during absorbance measurement, so the transmission of light may have been obstructed, resulting in an absorbance value higher than the actual value.
When a clear abnormality during measurement can be confirmed in this way, it provides a basis for excluding the measured value.
However, when excluding the value, the reason must be clearly stated, and if possible, the measurement should be repeated under the same conditions for confirmation.

When an Outlier Should Not Be Excluded

An outlier should not be excluded when there is no clear reason for doing so.
Reasons such as “it is far from the mean,” “it does not fit the regression line,” “excluding it increases R2,” or “the results look cleaner” are not sufficient grounds for exclusion.
An outlier is also data obtained from the experiment and should not be removed merely for convenience.

For an outlier of unknown cause, first check the operational records and, if remeasurement is possible, repeat the measurement.
If remeasurement is not possible, present the results including that value and discuss it as a cause of increased variation in the measured values.
The decision not to exclude an outlier is also scientifically important.

Example Discussion:
It is not appropriate to exclude a measurement point solely because it deviates from the regression line.
If no clear operational error or measurement abnormality can be confirmed, the value must also be treated as part of the experimental results.
Therefore, in this experiment, the outlier was not excluded and was discussed as a factor that increased the variation in the measured values.

Relationship Between Outliers and the Mean

Outliers have a large effect on the mean.
Particularly when the number of measurements is small, a single outlier can greatly increase or decrease the mean.
Therefore, when using the mean as a representative value, it is necessary to check whether outliers are present.

If the mean including the outlier differs greatly from the mean excluding it, the outlier can be considered to have a large effect on the conclusion.
However, the fact that the mean changes greatly does not by itself justify excluding the outlier.
Exclusion requires an operational or measurement-based reason.

Example Discussion:
Because the mean changed greatly when the outlier was included, this value is considered to have had a large effect on the representative value of the overall results.
Particularly when the number of measurements is small, even a single outlier can cause a large shift in the mean.
However, it is not appropriate to exclude an outlier solely because it has a large effect on the mean; clear evidence of a measurement abnormality or operational error is required for exclusion.

Relationship Between Outliers and Standard Deviation

When an outlier is included, the standard deviation increases.
Because standard deviation indicates how widely the measured values are distributed around the mean, even a single value that deviates greatly can make the overall variation appear large.
As a result, reproducibility may be evaluated as low.

If the standard deviation increases because of an outlier, its cause must be discussed.
If the outlier was caused by an operational error, remeasurement or exclusion may be considered, but if the cause is unknown, it should be treated as a result with large variation in the measured values.
It is useful to explain the reason for the large standard deviation in relation to the outlier.

Example Discussion:
Because one measured value deviated greatly from the other values, the standard deviation is considered to have increased.
Because standard deviation is an indicator of variation in measured values, it is strongly affected by outliers.
If the cause of this outlier is unclear, it should not be excluded and should instead be discussed as a factor that reduced reproducibility.

Outliers in Calibration Curves

In a calibration curve, the relationship between the concentration of standard solutions and the measured signal is represented by a regression line.
If only one point deviates greatly from the regression line, that point may be an outlier.
Possible causes include errors in dilution of the standard solution, contamination of the cell, bubbles, abnormal instrument readings, and errors in peak integration.

Outliers in a calibration curve affect the slope, intercept, R2, and calculation of the concentration of an unknown sample.
In particular, if a point at the low- or high-concentration end deviates, the slope of the entire regression line may change greatly.
Because outliers in a calibration curve directly affect quantitative results, they must be handled carefully.

Example Discussion:
A possible cause of some points on the calibration curve deviating greatly from the regression line is an error in the dilution procedure for the standard solution.
Including this point changes the slope, intercept, and R2 of the regression line and also affects the calculation of the concentration of the unknown sample.
Therefore, the cause of an outlier on a calibration curve should be investigated, and if necessary, the standard solution should be prepared again and the measurement repeated.

How to Handle Points That Deviate from the Regression Line

If there is a point that deviates from the regression line, consider why it deviated rather than immediately excluding it.
If the deviation occurs on the high-concentration side, it may be caused by saturation of the detector response or measurement outside the linear range.
If the deviation occurs on the low-concentration side, noise or the effect of the blank value may have been large.

If a point deviating from the regression line indicates a problem with the measurement range, rather than excluding only that point as an outlier, it is necessary to reconsider the range over which linearity is valid.
A deviating point may provide important information about the limits of the experimental conditions or measurement range.

Example Discussion:
If a measurement point on the high-concentration side deviated from the regression line, the measurement signal may have become saturated, causing the linear relationship between concentration and signal to break down.
In this case, rather than simply excluding the point as an outlier, it is necessary to consider the possibility that it exceeded the linear range of the calibration curve.
Therefore, it is desirable to limit the analysis to the concentration range in which linearity can be confirmed.

Outliers in Titration Experiments

In titration experiments, only one of several titration volumes may deviate greatly.
Possible causes include adding titrant beyond the endpoint, incorrectly reading the burette, bubbles being present, using the wrong sample amount, or differences in judging the color change of the indicator.

In titration, a difference of even one drop near the endpoint can affect the result.
If there is a record showing that the endpoint was clearly exceeded by a large amount, this provides a basis for treating the value as an outlier.
On the other hand, if the value is only slightly different from the others, it is often included and discussed as variation in the procedure.

Example Discussion:
A possible reason why only one titration value was larger than the others is that too much titrant was added after passing the endpoint.
If the endpoint is exceeded, the titration volume becomes larger than the actual value, which also affects the calculated concentration.
If the operational record confirms that the endpoint was greatly exceeded, this provides a basis for treating the measured value as an outlier.

Outliers in Absorbance Measurements

In absorbance measurements, contamination of the cell, bubbles, fingerprints, sample turbidity, deviations in blank correction, insufficient sample mixing, and incorrect wavelength settings can cause outliers.
Because absorbance is sensitive to the condition of light transmission, even small bubbles or contamination can greatly change the value.

If an absorbance outlier occurs, check the condition of the cell and the circumstances during measurement.
If bubbles or contamination are confirmed, remeasurement is desirable.
If no abnormality during measurement can be confirmed, the preparation of the sample concentration and the mixing condition should also be considered.

Example Discussion:
A possible cause of one absorbance value deviating greatly from the other measured values is bubbles inside the cell or contamination on the surface of the cell.
Bubbles and contamination may interfere with the transmission of light and cause the absorbance to be higher than the actual value.
Therefore, when an outlier occurs in absorbance measurement, it is necessary to clean the cell, remove any bubbles, and repeat the measurement.

Outliers in Mass Measurements

In mass measurements, spilling the sample, moisture absorption, insufficient drying, static electricity, air currents around the balance, failure to close the draft shield, errors in subtracting the tare, and adhesion to the container can cause outliers.
Particularly with small samples, even slight adhesion or spillage can greatly affect the measured value.

When discussing an outlier in mass measurement, check whether the sample was sufficiently dried, whether it absorbed moisture during weighing, and whether any sample remained in the container.
Reading the balance before the display stabilizes may also produce an outlier.

Example Discussion:
Possible causes of the mass measurement deviating greatly from the other measured values include moisture absorption by the sample or loss due to adhesion during weighing.
If the sample absorbs moisture, its mass increases, whereas spilling or adhesion during transfer decreases the mass.
To prevent outliers in mass measurements, it is important to dry the sample sufficiently, store it in a desiccator, and take the reading only after the balance display has stabilized.

Outliers and Remeasurement

When an outlier is found, the most desirable response is to repeat the measurement.
Remeasurement makes it possible to determine whether the deviating value was an accidental measurement abnormality or a phenomenon that occurs again under the same conditions.
If the remeasured value agrees with the other values, the initial outlier is more likely to have been caused by an operational error or measurement abnormality.

On the other hand, if a similar value is obtained even after remeasurement, the value may not be an outlier but may instead reflect the experimental conditions or properties of the sample.
If remeasurement is not possible, present the results including the outlier and discuss the large uncertainty.

Example Discussion:
When an outlier is observed, remeasurement can be performed to determine whether the value was caused by a temporary operational error or whether it is a reproducible result.
If the remeasured value agrees with the other measured values, the initial outlier is likely to have been caused by an abnormality during measurement.
On the other hand, if a similar value is obtained upon remeasurement, the value should not simply be excluded as an outlier, and the experimental conditions and properties of the sample should be reconsidered.

How to Write Results That Include an Outlier

If an outlier is not excluded, show the mean and standard deviation including that value and discuss how the outlier increased the variation.
If the cause of the outlier is unclear, it is appropriate to write that “the cause could not be identified, but it had a large effect on the variation in the measured values.”

Results that include an outlier may be treated as having low reproducibility.
However, this is not a bad thing; it is important because it honestly presents the experimental results.
Including an outlier may also reveal problems with the measurement method or operational conditions.

Example:
One value deviated greatly from the other measured values, but no clear operational error during measurement could be confirmed.
Therefore, this value was not excluded, and the mean and standard deviation were calculated including it.
Due to the effect of the outlier, the standard deviation increased, leaving uncertainty regarding the reproducibility of this measurement.

How to Write Results When an Outlier Is Excluded

If an outlier is excluded, always state the reason for exclusion.
For example, clearly state the operational basis, such as “because bubbles were observed in the cell during measurement,” “because the sample was spilled,” or “because the titration endpoint was greatly exceeded.”
In addition, showing how the results changed before and after exclusion increases the transparency of the data processing.

When writing about the exclusion of an outlier, it is important not to give the impression that the value was excluded because doing so improved the results.
State the basis for determining that the outlier was not a valid measurement obtained under the same conditions and, if possible, also include the remeasurement result.

Example:
For the measurement that produced the outlier, it was recorded that titrant addition was stopped only after the titration endpoint had been greatly exceeded.
Therefore, this measured value was difficult to regard as a valid titration value obtained under the same conditions and was excluded from the calculation of the mean.
After exclusion, the remaining measured values agreed well with each other and the standard deviation also decreased, so the remaining measured values were considered to be reproducible results.

Statistical Tests for Outliers

Statistical tests may be used as a method for identifying outliers.
For example, there are methods for determining whether a value can statistically be considered an outlier based on the number of measurements and assumptions about the distribution.
However, in basic laboratory reports, whether statistical tests should be used must be determined according to the laboratory manual or the instructions of the instructor.

Even if a value is statistically determined to be an outlier, it is still necessary to consider why that value occurred.
Conversely, excluding a value based only on intuition without performing a statistical test should be avoided.
It is important to consider the handling of outliers based on both numerical judgment and operational records.

Example Discussion:
Statistical tests can be used to identify outliers, but whether a value may be excluded must follow the instructions in the laboratory manual or those of the instructor.
Even when a statistical test indicates the possibility of an outlier, it is important to check whether an operational error or abnormal measurement condition may have caused it.
Therefore, the handling of outliers should be determined not only by numerical evaluation but also in combination with records of the experimental procedure.

Difference Between Excluding Outliers and Data Falsification

Excluding an outlier without a valid reason is problematic in the handling of data.
If values that do not fit the experimental results are conveniently removed, the results may appear cleaner than they actually are and may lead to an incorrect conclusion.
When excluding an outlier, always clarify the reason and procedure, and retain the original data when necessary.

Discussing outliers is an important part of handling data honestly.
The presence of an outlier itself does not mean that the experiment failed.
Rather, by not hiding the outlier, considering its cause, and explaining its effect on the results, the reliability of the report is increased.

Important:
Outliers must not be deleted without a clear reason.
If an outlier is excluded, evidence such as an abnormality during measurement, an operational error, a statistical judgment, or a remeasurement result must be provided.

Example Discussion:
An outlier is part of the experimental results, and it is not appropriate to exclude it simply because it is inconvenient.
Excluding an outlier requires clear evidence such as an operational error or measurement abnormality.
If there is no such evidence, it is important to present the results including that value and discuss it in terms of variation in the measured values and reduced reproducibility.

Causes of Error That Produce Outliers

Causes of error that produce outliers include sample preparation errors, concentration calculation errors, insufficient sample mixing, unstable measuring instruments, contaminated equipment, bubbles, errors in endpoint judgment, insufficient drying, moisture absorption, recording errors, and unit conversion errors.
These errors may cause only a specific measured value to deviate greatly.

When an outlier occurs, check whether the value is too large or too small.
If it is too large, possible causes include overtitration, residual solvent, contamination by impurities, and increased background signal.
If it is too small, possible causes include sample loss, insufficient sample collection, incomplete reaction, and insufficient measurement.
Considering the cause based on the direction in which the value deviated leads to a more specific discussion.

Example Discussion:
Possible reasons why the outlier was larger than the other measured values include adding too much titrant or contamination of the sample with impurities.
On the other hand, if the outlier was smaller, insufficient sample collection or loss during transfer may have been the cause.
When discussing an outlier, it is necessary to check in which direction the value deviated and consider the cause in relation to the experimental procedure.

When the Results Can Be Considered Good

From the perspective of outliers, results can be considered good when multiple measured values agree well and there are no obvious outliers.
In this case, the operational and measurement conditions can be considered stable and the reproducibility high.
In addition, if the standard deviation is small, the variation in the measured values can also be considered small.

However, the absence of outliers does not necessarily mean that the values are close to the theoretical value.
If all measured values are shifted in the same direction, a systematic error may be present.
Whether the results are good should be judged not only by the presence or absence of outliers but also by considering the mean, standard deviation, and difference from the theoretical value.

Example Discussion:
All of the measured values were close to the mean, and no obvious outliers were observed.
This suggests that the measurement procedure was stable and reproducibility was good.
However, the absence of outliers does not guarantee that the measured values are close to the theoretical value, so the mean must also be compared with the theoretical value.

Example Discussions When the Experiment Did Not Go Well

When an outlier occurs, discuss not only whether the outlier should be included or excluded, but also why it occurred.
If an operational error is clear, provide the basis for exclusion or remeasurement.
If the cause is unknown, present the result including the outlier and discuss it as a factor that reduced reproducibility.

Example Discussion:
Only one of the measured values deviated greatly from the other values.
A possible cause is that the sample was collected without being sufficiently mixed, resulting in a higher concentration only in that measurement.
Because this outlier caused large changes in the mean and standard deviation, the sample should have been mixed uniformly before measurement.

Another Example Discussion:
For the measurement that produced the outlier, the operational record confirmed that titrant was added well beyond the endpoint.
Therefore, this value can be judged not to be a valid titration value obtained under the same conditions.
If it is excluded, the reason must be clearly stated, and if possible, the validity of the value should be confirmed by remeasurement.

Another Example Discussion:
A measurement point that deviated from the regression line was observed, but no clear abnormality during measurement could be confirmed.
Therefore, the point was not readily excluded, and possible effects of errors in preparing the standard solution or problems with the measurement range were considered.
Because the outlier reduced R2, remeasurement or preparation of the standard solution again is necessary.

How to Write Points for Improvement

In discussing outliers, it is important not only to estimate their causes but also to describe improvements that can prevent similar outliers from occurring in the future.
Points for improvement are easier to write if they are organized into sample preparation, measurement procedure, equipment checks, recording, remeasurement, and data processing.

Improvements to Experimental Procedures

  • Mix the sample thoroughly before collecting it
  • Use pipettes and volumetric flasks correctly
  • Add titrant slowly near the endpoint during titration
  • Check for bubbles and contamination in the cell during absorbance measurement
  • Transfer samples carefully to avoid spilling them during mass measurement
  • Take readings only after the balance or measuring instrument has stabilized
  • Keep reaction time and temperature consistent
  • Thoroughly clean and dry equipment

Improvements to Data Processing

  • Record all measured values
  • Record the circumstances during the measurement in which the outlier occurred
  • If an outlier is excluded, clearly state the basis for exclusion
  • Compare results including the outlier with results excluding it
  • Repeat the measurement if possible
  • Show not only the mean but also the standard deviation
  • Check the effect on the regression line and R2
  • Follow the rules for handling outliers specified by the instructor or laboratory manual

Example of How to Write Points for Improvement:
To prevent outliers, it is important to mix the sample thoroughly, keep the measurement conditions consistent, and record any abnormalities during measurement.
In addition, when an outlier occurs, its cause should be investigated before exclusion, and remeasurement should be performed if possible.
In data processing, comparing the results including the outlier with those excluding it and clearly stating the basis for exclusion can improve the reliability of the results.

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of outliers, simply writing “there was an outlier” or “it was excluded” results in a superficial discussion.
A good discussion explains what the outlier affected, why it may have occurred, and whether there is a basis for excluding it.

Superficial Discussion Good Discussion
There was an outlier. Only one point deviated greatly from the other measured values, and it may have been caused by insufficient sample mixing or an operational error during measurement.
The outlier was excluded. Because bubbles were observed in the cell during measurement and the absorbance was likely overestimated, there is a basis for excluding that measured value.
It was a strange value, so it was deleted. If no clear operational error can be confirmed, it is not appropriate to exclude a measured value solely because it does not fit the regression line.
The outlier increased the standard deviation. Including the outlier increased the standard deviation and had a large effect on the evaluation of the reproducibility of the measured values as a whole.
I will be more careful next time. Next time, abnormalities during measurement should be recorded, remeasurement should be performed if an outlier occurs, and the basis for exclusion should be clearly stated if the value is excluded.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of outliers.
Adjust the necessary parts according to your own experimental results.

  • An outlier is a value that deviates greatly from the trend of other measured values.
  • Possible causes of the outlier include errors in the measurement procedure and sample inhomogeneity.
  • Outliers have a large effect on the mean and standard deviation.
  • Excluding an outlier requires clear evidence such as an operational error or measurement abnormality.
  • It is not appropriate to exclude a value solely because it deviates from the regression line.
  • If the clear cause is unknown, the results should be presented including the outlier.
  • When an outlier is included, the standard deviation increases and reproducibility is evaluated as lower.
  • An outlier on a calibration curve affects the slope, intercept, R2, and quantitative value of an unknown sample.
  • When an outlier is observed, it is desirable to repeat the measurement under the same conditions if possible.
  • If an outlier is excluded, the reason for exclusion and the results before and after exclusion must be clearly stated.

Points to Check When Discussing Outliers

Checking the following points before writing the report makes it easier to write the discussion.

  • Is the value considered to be an outlier clearly identified?
  • Have all measured values been recorded?
  • Has the effect of the outlier on the mean been checked?
  • Has the effect of the outlier on the standard deviation been checked?
  • Has the effect on the regression line and R2 been examined?
  • Is there a record of abnormalities or operational errors during measurement?
  • Is there a clear basis for exclusion?
  • Has the value been excluded without a valid basis?
  • Has the possibility of remeasurement been checked?
  • Have the results including the outlier and excluding the outlier been compared?
  • Has the effect on the conclusion been considered?
  • Do the points for improvement correspond to the cause of the outlier?

Summary

An outlier is a value that deviates greatly from the trend of other measured values or a regression line.
Outliers may be caused by operational errors or measurement errors, but they may also be important data indicating sample inhomogeneity, limitations of the measurement range, or unexpected reactions.
Therefore, when an outlier is found, it is important to first investigate the cause rather than immediately excluding it.

An outlier may be excluded when there is clear evidence, such as spilling the sample, greatly exceeding the endpoint, bubbles being present in the cell, an instrument error occurring, or a recording error being made.
On the other hand, it is not appropriate to exclude a value solely because it is far from the mean, does not fit the regression line, or makes the results look poor.
If the cause is unknown, present the results including the outlier and discuss it in terms of variation in the measured values and reduced reproducibility.

In a report, rather than simply writing that “the outlier was excluded,” organize and discuss the cause of the outlier, its effect on the mean, standard deviation, and calibration curve, the basis for exclusion, whether remeasurement was performed, the reason for not excluding it, and points for improvement.
The handling of outliers is extremely important for interpreting experimental data honestly and scientifically.

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