SCIENTIFIC
MEASUREMENT
OBJECTIVE:
•explain the difference between
mass, volume, and density of a
solid using the correct and
appropriate units;
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MEASUREMENT- process of
determining the size, quantity,
or extent of something, often by
comparing it to a standard
unit. It involves assigning a
numerical value to a physical
quantity, like length, mass, or
time. this process is
fundamental to science,
engineering, and everyday life.
MEASUREMENT:
- is the quantification of
attributes of an object or event.
- it's the act of comparing an
unknown quantity with a known
standard quantity of the same
kind.
-the result of measurement is a
numerical value with associated
units.
KEY ASPECTS:
Quantifying Attributes: Measurement allows us to express the
characteristics of objects or events numerically.
•Comparison: It involves comparing an unknown quantity to a
reference standard.
•Units: Measurements are expressed using standard units like
meters, kilograms, seconds, etc.
•Types of Measurements: Common measurements include
length, mass, volume, time, and temperature.
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Examples:
•Using a ruler to determine the
length of a piece of paper.
•Using a scale to find the weight of
an object.
•Using a stopwatch to measure the
time it takes to run a race
.
IMPORTANCE:
•Measurement is crucial for scientific research, enabling
precise observations and data collection.
•It is essential in engineering and construction for ensuring
accuracy and safety.
•Measurement plays a role in everyday activities, from
cooking to shopping.
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THE SEVEN BASE UNITS OF THE INTERNATIONAL SYSTEM
OF UNITS (SI) ARE:
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TO MEASURE CORRECTLY,
1. CHOOSE THE RIGHT TOOL FOR THE
JOB,
2. ALIGN IT ACCURATELY, AND
3. READ THE MEASUREMENT
CAREFULLY,
ENSURING YOU'RE ACCOUNTING FOR
ANY POTENTIAL ERRORS OR
VARIATIONS IN THE TOOL ITSELF.
ELABORATION:
Selecting the Right Tool:
•For small objects, a ruler or measuring
tape is suitable.
•For larger objects or distances,
a tape measure or even
specialized tools might be
necessary.
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2. Preparing for Measurement:
•Flat Surface:
•Place the object on a flat, stable surface to avoid inaccuracies.
•Alignment:
•Align the measuring tool's starting point (usually zero) with one
• end of the object.
•Straightness:
•Ensure the measuring tool is straight and parallel to the object
• being measured.
•Eye Level:
•When reading the measurement, position your eyes directly
above the point on the measuring tool where the object ends,
to avoid parallax errors.
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3. Taking the Measurement:
1. Read Carefully: Note the measurement
where the object ends on the ruler or tape
measure.
2. Units: Always include the units of
measurement (e.g., inches, centimeters).
3. Double-Check: Repeat the measurement to
confirm its accuracy.
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ACCURACY VS. PRECISION
Accuracy refers to how close a
measurement is to the true or
accepted value.
Precision refers to how close
multiple measurements of the
same item are to each other.
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QUANTIFYING QUALITY: PERCENT ERROR
• We use Percent Error to mathematically calculate exactly how
accurate our data is.
• It compares your experimental laboratory results against the
known theoretical value.
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WHY ONE TRIAL IS NEVER ENOUGH
• Single-Trial Trap: Running a test once leaves your data
vulnerable to random environmental fluctuations and
sudden human blunders.
• Error Minimization: Multiple replication trials allow
errors to balance out mathematically via averages.
• True Quality Check: You cannot declare data "precise"
if you only have one individual data point to look at!
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WHAT IS A MEASUREMENT ERROR?
• A measurement error is the difference between a measured
value and the true value of the quantity being measured.
• These errors can arise from instrument limitations, human
mistakes, environmental factors, or procedural flaws.
• For instance, a technician entering a wrong reading or using
an improperly calibrated micrometer can lead to a
measurable error.
• Understanding errors helps improve quality control, maintain
regulatory compliance, and prevent costly engineering
failures.
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PRACTICAL EXAMPLES OF MEASUREMENT ERRORS
• A scale error in measurement may happen if the measuring
scale itself is miscalibrated.
• Human error in measurement includes parallax errors,
misreading instruments, or data entry mistakes.
• Instrumental errors come from worn-out, poorly maintained,
or incorrectly calibrated instruments.
• A gross error example is reading a value while the
instrument is off-zero
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TYPES OF ERRORS IN MEASUREMENT
• Gross Errors: Gross errors result from human mistakes
• Misreading measurement scales
• Recording incorrect values
• Using faulty techniques
• Example: Writing “16.3 mm” instead of “13.6 mm.”
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TYPES OF ERRORS IN MEASUREMENT
• Systematic Errors: These are predictable and repeatable
errors due to flaws in the measuring system or
methodology:
• Instrument calibration drift, uncalibrated equipment
• Environmental interference (e.g., humidity, temperature)
• Faulty measurement setup, incorrect formula used
• Example: A pressure gauge that consistently reads 5 psi
higher due to zero error.
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TYPES OF ERRORS IN MEASUREMENT
• Random Errors(Indetermined): These occur unpredictably
and vary with each measurement, often caused by:
• Minute fluctuations in the environment
• Observer variability
• Equipment resolution limits
• Example: A digital balance showing slightly different
weights each time for the same sample.
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WHAT CAUSES MEASUREMENT ERRORS?
• The sources of error in measurement include
• Personal errors – mistakes by the person performing the
measurement.
• Instrumental errors – due to faulty or poorly calibrated equipment.
• Environmental errors– changes in temperature, humidity, or
pressure.
• Observational errors – limitations in the observer’s ability to read
instruments accurately.
• Knowing the source allows engineers and technicians to take
preventive or corrective action
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HOW TO REDUCE ERRORS IN MEASUREMENT
• Calibrate instruments regularly to traceable standards (e.g.,
ISO/IEC 17025)
• Use high-precision, well-maintained tools
• Train operators to minimize observational and procedural
mistakes
• Control environmental conditions in metrology labs or test
stations
• Additionally, applying error analysis and uncertainty budgets
ensures consistent accuracy across test and production
environments.
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UNDERSTANDING ERROR PROPAGATION AND PERCENT ERROR
• When combining multiple measurements, their errors
propagate:
• Addition/Subtraction: Add absolute errors
• Multiplication/Division: Add percentage errors
• Powers/Exponents: Multiply relative error by exponent
• Example: If a length measurement is 10.0 ± 0.2 cm and
width is 5.0 ± 0.1 cm, then area = 50.0 cm² with a
propagated error of ±2.5%.
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•Also consider:
•Absolute error: |Measured – True|
•Relative error: (Absolute / True)
•Percentage error: Relative × 100
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CLOSING THOUGHTS ON MEASUREMENT ERRORS
• Understanding and minimizing measurement errorswhether gross, systematic, or random – is fundamental for
ensuring reliable data. Whether caused by instrument faults,
environmental changes, or human limitations, every error
tells a story about your system’s accuracy.
• By identifying errors early and applying the right corrective
strategies, professionals across research, manufacturing,
and quality control can enhance confidence in their
measurements and maintain process excellence.
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THANK
YOU
ACCURACY
AND
PRECISION
IMPORTANCE OF ACCURACY AND
PRECISION IN MEASUREMENT
ACCURACY AND PRECISION
ACCURACY REFERS TO
HOW CLOSE A
MEASUREMENT IS TO
THE TRUE OR
ACCEPTED VALUE. A
HIGHLY ACCURATE
MEASUREMENT
REFLECTS THE ACTUAL
QUANTITY BEING
MEASURED.
Precision: Precision refers
to how close repeated
measurements of the
same quantity are to each
other. A precise
measurement shows
consistency and
reproducibility, even if it
isn't necessarily close to
the true value.
IMPORTANCE OF
ACCURACY:
RELIABLE RESULTS: ACCURATE
MEASUREMENTS ARE ESSENTIAL
FOR OBTAINING RELIABLE AND
MEANINGFUL RESULTS.
INACCURATE MEASUREMENTS
LEAD TO ERRORS IN
CALCULATIONS AND
CONCLUSIONS, POTENTIALLY
INVALIDATING THE ENTIRE
RESEARCH OR PROJECT.
IMPORTANCE OF
ACCURACY:
VALID CONCLUSIONS:
ACCURACY IS CRITICAL FOR
DRAWING VALID
CONCLUSIONS AND MAKING
INFORMED DECISIONS BASED
ON EXPERIMENTAL DATA OR
OBSERVATIONS.
IMPORTANCE OF
ACCURACY:
CORRECT INTERPRETATION:
ACCURATE MEASUREMENTS
ALLOW FOR THE CORRECT
INTERPRETATION OF DATA
AND AVOID
MISINTERPRETATIONS THAT
COULD LEAD TO WRONG
CONCLUSIONS.
IMPORTANCE OF
ACCURACY:
EFFECTIVE DECISION MAKING: IN
MANY FIELDS, DECISIONS ARE
MADE BASED ON
MEASUREMENTS. ACCURATE
MEASUREMENTS ARE ESSENTIAL
FOR MAKING EFFECTIVE
DECISIONS, ESPECIALLY IN
CRITICAL AREAS LIKE MEDICINE,
ENGINEERING, AND FINANCE.
IMPORTANCE OF PRECISION:
Reproducibility: Precise measurements are
reproducible; other researchers should be able to
repeat the experiment and obtain similar results.
This reproducibility is essential for validating
findings and ensuring the reliability of scientific
knowledge.
IMPORTANCE OF PRECISION:
Uncertainty Quantification: Precision allows
for a better understanding of the uncertainty
associated with the measurements. High
precision means that the measurements are
clustered closely together, indicating less
variability.
IMPORTANCE OF PRECISION:
Identifying Systematic Errors: While precision
doesn't guarantee accuracy, a lack of precision can
be an indicator of systematic errors within the
measurement process. If measurements are not
precise, it suggests that there are consistent biases
affecting the results.
IMPORTANCE OF PRECISION:
Confidence in Results: High precision
increases confidence in the results, as it
shows that the measurements are
consistent and reliable.
RELATIONSHIP BETWEEN
ACCURACY AND PRECISION:
Ideally, measurements should be both accurate and precise.
However, it's possible to have high precision without high
accuracy (e.g., consistently measuring the same incorrect value)
and vice versa (e.g., getting the correct value only occasionally).
The goal in any measurement process is to strive for both high
accuracy and high precision. This requires careful attention to
experimental design, proper calibration of instruments, and the
use of appropriate techniques.
IDENTIFYING AND REDUCING MEASUREMENT
ERRORS
MEASUREMENT ERROR
DIFFERENCE BETWEEN SYSTEMATIC AND
RANDOM ERRORS WITH EXAMPLES:
• Systematic Error Example: A balance that
is not properly calibrated consistently
gives readings that are 0.1g too high.
• Random Error Example: Variations in
reading a burette due to parallax error.
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 SOURCES OF SYSTEMATIC ERRORS
A.) incorrect calibration of instruments like
(balances, volumetric glasswares)
B.) instrumental drift (temperature changes
affecting reading)
C.) personal bias (consistently over estimating
or understimating readings)
D.) impurities in reagents
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SOURCES OF RANDOM ERRORS:
a.) reading errors (parallax, estimation
b.) environmental fluctuations
(temperature, pressure)
c.) limitation of instruments’ precision
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IMPROVING MEASUREMENT RELIABILITY
• Calibration of instruments
• Proper use of instruments (parallax correction)
• Multiple measurements and averaging
• Using more precise instruments
• Controlling environmental conditions
• Using appropriate techniques (e.g., proper
titration technique).
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EXAMPLES OF
Reading a scale:
RANDOM ERRORS
Reaction time:
IN SCIENCE
EXPERIMENTS?
Environmental fluctuations
Instrument limitations:
Natural variations
Random sampling
DIFFERENCE BETWEEN SYSTEMATIC AND RANDOM ERRORS
Feature
Random Error
Systematic Error
Nature
Unpredictable, inconsistent variations
Consistent, repeatable deviations
Cause
Multiple, small, uncontrollable factors
Specific, identifiable source(s)
Effect on
Data
Scattered data points around the true
value
Data points consistently shifted from
true value
Sign
Positive or negative, unpredictable
Consistently positive or negative
Magnitude
Varies from measurement to
measurement
Relatively constant across
measurements
Reduction
Averaging multiple measurements,
improved technique
Instrument calibration, improved
procedure
Examples
Fluctuations in reading a scale, slight
variations in reaction time
Faulty instrument calibration,
consistent bias in reading a scale
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1. Cooking and Baking:
EXAMPLES OF
MEASUREMENT• Incorrect ingredient measurements: Using a cup instead
of a measuring cup, or eyeballing amounts, can lead to
ERRORS IN
cakes that don't rise properly or sauces that are too thick
EVERYDAY
or thin. This is a form of random error, as the inaccuracy
varies each time.
LIFE?
• Faulty oven temperature: An oven that consistently runs
hotter or colder than the set temperature introduces
systematic error, leading to consistently overcooked or
undercooked food.
• Inaccurate measuring spoons/cups: If your measuring
spoons are worn or improperly sized, this will introduce
systematic error.
1. Driving and Navigation:
EXAMPLES OF
MEASUREMENT Estimating distances: Incorrectly judging distances
when parking or changing lanes introduces
ERRORS IN
random error.
EVERYDAY
Misreading speedometers/odometers: A faulty
LIFE?
speedometer could lead to systematic error in
judging speed and distance traveled.
Incorrect GPS coordinates: GPS signals can be
affected by atmospheric conditions or
obstructions, introducing random error in location
information.
Personal Health:
EXAMPLES OF
MEASUREMENT Inaccurate weight measurements: A
ERRORS IN
malfunctioning scale will introduce
systematic error.
EVERYDAY
Improperly calibrated blood pressure
LIFE?
monitor: This introduces systematic error,
potentially leading to misdiagnosis.
Estimating portion sizes: Eyeballing food
portions for diet tracking leads to random
error.
Time Management:
EXAMPLES OF
MEASUREMENT Inaccurate clocks or watches: A
ERRORS IN
consistently fast or slow clock
EVERYDAY
introduces systematic error in
LIFE?
scheduling.
Misjudging time spent on tasks: This is
a source of random error, as the
inaccuracy in estimating time changes
from task to task.
Yes, many measurement errors
can be avoided or significantly
ARE THERE
ANY
reduced through careful
MEASUREMENT planning and execution. The
ERRORS THAT
key
is
understanding
the
CAN BE
sources of error and
AVOIDED?
implementing appropriate
strategies.
AVOIDABLE SYSTEMATIC ERRORS:
• Instrument Calibration: Many systematic errors stem from improperly
calibrated instruments. Regular calibration of tools like scales, thermometers,
measuring tapes, and other instruments ensures accurate readings. This is
arguably the most important step in preventing systematic error.
• Environmental Factors: Some systematic errors arise from uncontrolled
environmental conditions. For example, temperature fluctuations can affect
the accuracy of some measurements. Controlling the environment (e.g.,
using a temperature-controlled room) minimizes these errors.
• Procedural Errors: Following established procedures correctly minimizes
systematic errors caused by improper techniques. This includes using correct
measurement techniques (avoiding parallax error when reading a graduated
cylinder, for example), using appropriate safety measures, and handling
samples correctly.
• Reagent Purity: In scientific settings, impure reagents are a significant source
of systematic error. Using high-purity reagents helps avoid this.
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AVOIDABLE RANDOM ERRORS
• Multiple Measurements: Taking multiple measurements and averaging
the results reduces the impact of random errors. The more measurements
you take, the closer the average will be to the true value.
• Improved Technique: Developing and using precise techniques
minimizes random errors associated with human error. This includes
careful observation, precise handling of equipment, and consistent
procedures.
• Using More Precise Instruments: Using instruments with higher precision
reduces random errors. For example, using a digital scale instead of an
analog scale will lead to more precise mass measurements.
• Statistical Analysis: Applying statistical methods (e.g., standard deviation)
to analyze data helps quantify the uncertainty associated with random
errors and improves the reliability of the results.
CAN WE ELIMINATE RANDOM ERRORS ENTIRELY?
• No, it's impossible to eliminate random
errors entirely. Random errors, by their very
nature, are unpredictable and arise from
numerous small, uncontrollable factors.
•
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FACTORS CAN ELIMINATE RANDOM ERRORS
• Limitations of instruments: Even the most precise instruments have inherent
limitations. There's always a degree of uncertainty in any measurement, no
matter how sophisticated the equipment.
• Fluctuations in environment: Slight variations in temperature, pressure, humidity,
or other environmental factors can subtly affect measurements. These
fluctuations are often difficult, if not impossible, to completely control.
• Human error: No matter how skilled a person is, there will always be some
degree of variability in their observations and manipulations. This includes
things like parallax error when reading a scale or slight variations in reaction
times.
• Intrinsic randomness in the system: Some systems are inherently random at a
fundamental level. For example, the exact decay time of a radioactive atom is
governed by probability and cannot be predicted with certainty, even with
perfect instrumentation.
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WHILE WE CAN'T ELIMINATE RANDOM ERRORS, WE CAN
REDUCE THEIR IMPACT THROUGH VARIOUS
TECHNIQUES, AS:
• Multiple measurements: Taking many measurements and
averaging the results reduces the effect of random errors because
random variations tend to cancel each other out.
• Improved technique: Careful experimental design and execution
minimizes human error and improves the consistency of
measurements.
• Higher precision instruments: Using more precise instruments
reduces the inherent uncertainty associated with the measurement
process itself.
• Statistical analysis: Statistical tools help quantify the uncertainty
associated with random errors and allow us to make more
informed conclusions.
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